There were a few other questions left and I asked a few natives to clarify them. If you have interest and work with KM2 you might find these as well difficult to understand.
tl;dr
あの人は、アメリカへ行ったきりだ。
* That person had gone to America and he/she will not come back for a while. This means we (or readers/listeners) assume that the person will not come back for a while, and the person’s feeling seems a little lonely. This sentence, for example, is used that a mother would say it to her son.*
*That person just (now) went to America.* <- Is this also a possible translation? Since きり means “just” as far as I read in the grammar book.
→ This expression is used only the person went to America a short time ago (a year ago) and he won’t come back for a while. This is not used when “he just went to America today”. 「きり」doesn’t mean “just” in this case. 「彼はアメリカに行って*しまって* (しばらくアメリカにいるだろう)」. Does this make sense?
→ Short time means a year for Japanese people, ok? lol It is difficult to mark this kind of usage of きり in the English sentence, but when talking, we could use intonation/rising voice to emphasize that it’s not a long time he went to America, implying, there is still something ahead waiting for him and he won’t come back so fast. Right?
学生であるかぎり、勉強するのは当然だ。
* As long as you are a student, it is quite natural that you should study. 「である限り」means “As long as~”*
社長は忙しいから、秘書を通じて頼んだほうがいい。
* Because the president is busy, you should ask via his secretary. 「秘書を通して」is the similar meaning of 「秘書に」. But 「秘書を通して」(ask through/via his secretary) is more a indirect way than 「秘書に」(ask his secretary), because the president was supposed to deal with his matter (but he can’t do this as he is busy). *
苦労した末の成功は、何よりもうれしいものだ。
* The success after experienced hardship is happy more than nothing. 「~した末」means “as a result of doing (something)”. 「末」also means “at the end of”.*
彼女は、何を聞いても笑っているきりで、答えない。
* She just smiles and wouldn’t answer my question(s) whatever I ask. 「きり」in this context, means “just”. She just smiles...*
雨や雪が降らないかぎり、毎日ジョギングを欠かさない。
* Unless it rains or snows, I go jogging every day. 「かぎり」in this case, “as long as it keeps doing/unless it does something...*
彼はよほど重病でないかぎりは、会社を休んだことがない。
* Except when he is ill badly, he goes to the office every day. 「かぎり」in this case, it means more like “Except/But/As long as”.*
ヘビースモーカーの彼は、たばこを1本吸い終わったか終わらないかのうちに、また次のたばこに火をつけた。
* He lit another cigarette in less than he had finished smoking the current one, as he is a heavy smoker. 「終わったか終わらないかのうちに」means here, that “doing something before or he has just finished” . This expression is used that he/she continues to do something. Right, in this case, he is a heavy smoker

* I suppose “No sooner he finished smoking one cigarette, he lit up a new one” is also possible, isn’t it? *
→ We could say “No sooner”.. but the nuance of this sentence will be different. 「終わったか終わらないかのうちに」is like “we don’t know whether he finishes or not, though, he started smoking another cigarette”. But the result will be the same because he can’t smoke another cigarette without finishing the current one.
→ Looking at another example using this construction:
チャイムが鳴るか鳴らないかのうちに、先生が教室に入って来た。
Just as the bell rang (= no sooner the bell had rang), the teacher entered the classroom. Right?
彼の言い方は進めているというより、強制しているようだ。
* The way he say seems to force to doing this, rather than recommend it. <-? You meant perhaps “The way he says it, seems rather he is forcing us than recommending us (to do/chose something)” → That’s right! Thanks!
頭がいい人ほど自慢しない。
* The more clever a person is, the less (?) it shows off. *
* Yes.
あの人は学者というよりタレントだ。
* This person is rather a star than a scholar. *
* Yes.
急に寒くなって、けさはもうコートを着ている人さえいた。
* (Some) People (even) wear coats this morning, as it gets colder suddenly. 「さえ」means like “even” so “Even some people wear coats”.
* さえ replaces が and は, so in this context, simplyfing the sentence, it would mean [...] 人がいる “there are people”. Would be “There are even people wearing already coats in this morning, as it became colder.” もいい?--> Ok. As long as ”さえ” implies “even” in the sentence.
予想に反した実験結果が出てしまった。
* The experimental result was observed than expected. 「反して」is “than we expected” . or 「予想以上に」is the same.
* The result of the experiment was different (in some neg. way due to しまった, I suppose), as expected, so “anti-expectationous”?
* “than we expected” is used both a negative and positive: The result was bad/good than we expected. “予想に反して” means 「予想していた以上に (than we expected) 」.
* Yeah, it can be like “Wow, that was (better) than expected by me!” or with a negative connotation like “The results against what we suspected (= had thought/anticipated) were published; he had cancer in fact.” <- Is that what you tried to explain?
この仕事は努力しただけ成果が現れるので、やりがいがある。
* It was worth doing this job, because the more I work harder the more I can gain my experiences. 「だけ」means here 「~したらしただけ/からすればするほど」.
新製品を開発するにあたり、強力なプロジェクトチームが作られた。
* A powerful project team was created in order to develop a new product. 「するにあたり」is “for/to/in order to”.
* “At the occassion of developing a new product” <- ?
* that’s right.
試合に出るからには、勝ちたい。
* Now that we participate in the game, we want to win the game!. 「からには」means 「と決まったからには」 = This is already decided (no one can change it), so the person’s mind should be set to do the thing.
安いからといって、そんなにたくさん買ってもむだだ。
* It is no use buying so many things even though they are cheap. 「からと言って」menas “even though/even if” = 「たとえそんなに安いからといっても」
あの車は形からすると10年ぐらい前のものだと思う。
* That car looks 10 years old, seeing from its form. = When you look at that car from its shape, the car is probably 10 years old. 「からすると」implies your assumption like “looks like”.
法律の上では平等でも、現実には不平等なことがある。
* Even if there is a fairness (legitimacy) under a law, there is an unfairness in reality. 「法の上では」「法の基では」. 「上」usually means “above/on” but in this case, under the law.
暗いわけだ。蛍光灯が1本切れている。
* No wonder it is dark. A fluorescent bulb was broken. 「どうりで~わけだ」= No wonder...
彼の気持ちがわからないわけでもありませんが、やはり彼の意見には賛成できません。
* It is not that I can’t understand his feeling, though, I can’t agree with his opinion. 「わからない(can’t understand)」& 「わけでもない(I don’t mean that)」are two negative verbs. If you use double negative verbs in a sentence, 「わけでもない」can be used. 「知らないわけでもないですが/が (It is not that I don’t know it..)」「言いたくないわけでもないですが/が (It is not that I don’t want to say this..)」. So you can’t say like “気持ちがわかるわけではない” because this is only one negative verb, so you should say “気持ちがわかる or 気持ちがわからない”.
* The informal variant is わけじゃないが, right? (Yes) F.e. ゴルフをしたくないわけじゃないが・・・ Is わけじゃん the same as わけじゃない? I suppose it’s just a short form? → 「わけじゃない」=「わけではない」. But 「わけじゃん」is different from 「わけじゃない」. 「気持ちがわからないわけじゃん」is like “You don’t understand me, do you” but it sounds like a dialog from somewhere in Japan

* Yeah, in her emails my girlfriend tends to use these じゃん forms quite often, so I was wondering. Your given example.. hm, is it something like:
「気持ちがわからないわけじゃん」 (it still has to be used with the negative verb in front of it, right? Like the other わけではない. Oh, before I forget, the わけでもありませんが is it the same as わけではない, or does it mean “It’s not that I don’t understand only his feelings, but also I cannot agree with his opinion”?) = 「気持ちがわからないでしょう(か?)。」 <- ?
先生は来週、お忙しいとか。お宅に伺うのは、再来週にしませんか。
* I heard the teacher will be busy next week. So why don’t we visit his/her house the week after the next? 「とか(聞いております)」: It implies “I heard”. So we can interpret this as “お忙しいという風に(ことを)聞いております”. *
* Then とか is a short, only used in letters, form of ~ということだ? *
→ You can use it in the spoken language, too. I guess it is used more often in spoken than written language. It’s very polite. And yes, it is the same as 「~ということ」
わたしは警官としてしなければならないことをしたにすぎません。
* I did only the thing that I should do as a police officer. 「~にすぎない/~したまで」means “just/only”. e.g. This area make up only a small part of the state. 「このエリアは州の一部を占めるにすぎない。This is just an example of my idea. 「これはただ私のアイディアの一部にしかすぎない」 *
酒の上でも、言ってはいけないことがある。
* Even though you are drunk, there is something you should not say. 「酒の上でも/酒の席であったとしても/酒の席だからと言って」= Even this is a place everyone drinks here...
* This sentence is still troublesome to me. I did not understand the content of your translation. I’d guess the sentence, intuitively, wants to say something like “When it is time of drinking sake (after sake was drunk), there are things that you shouldn’t say.” <-? *
→ Ok. This is more a cultural thing. When you drink a lot, you will feel strong and would become audacious (bold). But you should know what kind of thing you can say even when you are drunk and become audacious. If you can say a bad thing, you would hurt someone. But you can’t excuse due to drinks. You’d better be mature and have good manners when you drink. So 「酒の席であったとしても」.. even when you drink.... Does this make sense?
→ No, not really, sorry!

This is really difficult to comprehend, but perhaps we could work on this grammatical issue with the following explanation given in my grammar book:
その時、その場面、その条件の範囲で~だ、と言いたい時に使う。= ~上で(は)/~上の/~上でも/~上での
Well, the sentence above wants to say that at the time/occasion/condition (時・場面・条件) of drinking alcohol there are (indeed) things that should not be said. Is this, self-invented and self-made, example of me correct then?
f.e. 運転の上で(は?how would the sentence/meaning of the sentence be changed by attaching は here?)、携帯電話を使ってはいけません。
Or, using the ~上での construction, could I also say (like in a manual or a written piece? I guess nobody would use this sentence in spoken language?): 運転上での携帯電話の活用をしてはいけません。 <- ?
日本の会社で働く上で、注意しなければならないことは何でしょうか。
* On(In?/At?) work in a Japanese company, what we should be care for? 「働く上で/働くことにおいて」. the same meaning of “when I work in a Japanese company...”
* 日本の会社で働く時・・・ = 類語, only more formal?*
→ I think “日本の会社で働く上で” is more formal and well-written. It’s like “on”; on the matter / on the case; “On the case of working in a Japanese company” is more well-written than “When we work in a Japanese company”, isn’t it?!
→ Yep

In English we could say “When working at a Japanese company” rather then “When I work at a Japanese company”; I suppose in English it is only a matter of the sentence structure, whereas in Japanese you would use a more formal phrase instead of expressing the “when” by ~時 or ~たら, right? Are they “synonyms” otherwise in their meanings, apart from that they have a different level of formality?
日本から1日2時間A国向けの番組が放送されている。
* TV programs from Japan broadcasts towards country A for 2 hours a day. 「向け」= 「に向けて」「に対して」. 「日本からA国に向けたTV番組」
* From Japan there are 2 hours a day
* 向け = にとって? What’s the difference? I mean にとって means “for”, like 向け, but I from my “Japanese feeling”, the latter is more like “it’s especially aimed for these people (f.e. Koreans, Chinese, or series for old people etc.)”
病気の治療はもちろん、予防のための医学も重要だ。
* As well as/Not just a treatment of illenesses, medical for prevention is also important. 「~はもちろんのこと」: It goes without saying that... Or As well as... Or Not just... 「もちろん」means “of course” so this is like “病気の治療は, of course, (we’ve already considered)”.
有名人であればあるほどストレスも大きいのではないだろうか。
* The more one famous, the harder the person feel stressful. 「~であればあるほど、~だ」. This is an idiom in Japanese; The more …, the more... (in English)
窓を開けると、電車の音がうるさくてしようがない。
* Needless to say, there is train noise when I open the window. 「て(で)しょうがない」means “I can’t stand this happens” . I translated it “Needless to say” because there is no meaning/no change even we claim that noise.” . Meanwhile, 「しょうがない」means “Shit happens”.
* It is like “If I open the window, there will be noise from (outside) from the train (coming in), which can’t be helped (= I can’t make the trains stop in a way so that no noise will come in = naturally, then there will be noise, if I open the window lol). <- ? I ask because “Needless to say...” is - as I use and learnt it lol - 言うまでもないことですが、・・・ in Japanese
「あのレストランで送別会しない。」「あそこ50人入れるほど広かったっけ。」
* Can we have a farewell party at that restaurant? Is that (restaurant’s) capacity big enough to get around 50 people in? We use 「~っけ?」when we ask the thing to other (a friend). This is a colloquial. 「そうでしたっけ?」: Is that so?
「昨日、ジョンさんに会いましたよ。」「そうですか。ジョンさんといえばA社に就職が決まったそうですね。」
* I met John yesterday. I see. About John-san, I heard he got a job at company A. 「~と言えば」; when it comes to … / As for... / About ...
近々日本へいらしゃるとか。ぜひお会いしたいものです。<手紙>
* I heard you will be visiting Japanese in near future (soon?). I would love to see you. 「とか」in this case, we intrupt it 「日本へいらっしゃると聞いております」
* Talking about とか there is another usage, f.e. 食事をしたたかテレビを見たとか。 I ate lunch and watched TV and stuff.. = 食事視したりテレビを見たるした。?
その景色の美しさといったら、口で言い表せないほどです。
* It beyonds the description how beautiful the view was. 「美しさと言ったら」= 「美しさと言えば/については」. 「といったら~ほどです」is generally used.
* Talking of the beauty of the scenery, it was so (to that extent) [beautiful] that I cannot express it with my words. もいいですか。
→ OK.
これだけ捜しても見つからないのだから、あきらめるよりほかない。
* Having looked around such as long time, we might have to give up (we have no other clue except giving up). 「より他はない」= there is no way except doing this.
* Having looked around such a long time there is just giving up left. * もいいですか? OK
先生のお宅に、こんな夜中に電話するべきではない。
* We should avoid making a phone call in such a night time(?). 「べきではない」is simply “we shouldn’t do...” “We should avoid...”
= It’s morally/going after social rules, norms and values, not good and should not be done (= common sense) ?
言うべきことは遠慮しないではっきり言ったほうがいい。
* Things that ought to be said (one should say), should be said (you should say) without hesitation/reservation. *
* Yes!
国益に沿った外交政策が進められている。
* The diplomatic policy is directed towards national benefit. 「沿った」is “across/towards”. The diplomatic policy is progressed in order to gain a national benefit.
ビデオカメラが欲しくてしようがない。
* I am dying for a video camera. 「欲しくてしょうがない」= 「欲しくてたまらない」「すごく欲しい」
* I want a video camera, and I don’t know what to do about it (I’m so desperate getting one) もいいですか。
→ It’s stronger to say than “I want a video camera”. So sounds more like “I really want a video camera.”
医者の話し方からすると、わたしは、癌に違いありません。
* Assuming the way the doctor says, I must be a cancer. 「~に違いない」is “must be/might be”
今日の試合は優勝がかかっているだけに大勢のファンが詰めかけ熱烈な応援をしていた。
* Today’s game match is for the final match, so many fans came for the support. → ah... this is difficult to explain.. I will get back it later.
* だけに is difficult here, really

I tried making sense of it the whole night yesterday but tagged the card as “unknown” again.. Perhaps you can give me another example, when だけに is used like that above one?
さすがに最高級といわれるワインだけのことはある。味も香りも素晴らしい。
* This wine is not called the great wine for nothing. Both taste and flavor are beautiful/great. 「だけのことはある」= “not … for nothing”.
* だけのことはある = “not... for nothing” <- didn’t knew that

Thank you very much!
引っ越しの前の晩は、食事どころではなく、夜遅くまで荷作りが終わらなかった。
* On the night before the moving, (I was very busy for the packing), it was more than just meal (/ I didn’t have time to eat the dinner). I couldn’t finish packing until late the night. 「~どころではなく」means like 「~している暇はなく (I have no time to do...」
* Wasn’t sure about your translation here
Did you mean something like “On the night before moving, there was no time for eating (and besides that/in addition to that, or simply “and”) and we didn’t finish packing until late at night. <- ?
What is なく for a form of ない by the way? Like the masu-stem for enumerating things? f.e. 靴があり、かばんがあり、何でもがあります。 We have shoes, we have bags, we have anything.
値段が高いほど品物がいいとは限らない。
* It is not always true that expensive things are good value. 「~ほど~とは限らない」= It’s not always true that …
* Good to know that fixed phrase.. It just didn’t make any sense beforehand!
魚は新鮮でないかぎり、さしみにはできない。
* Unless fresh fishes, it is not good for sashimi. 「でない限り」「でなければ」: If it is not.../ Unless / Without...
彼は自分の考えが絶対であるかのように主張して譲らない。
* He wouldn’t compromise as if his idea is definite. 「であるかのように」 = as if...
息子の部屋の汚いことといったら、ひどいものです。
* When I say my son’s room is dirty, it is awful. 「と言ったら」is “When I say...”
* Finally this makes sense!

F.e. プレゼントがすごいものと言ったら、何か大きいです。 When I say it’s a sugoi-present, it IS something big/etc. <- ?
コンピューターが動かず、どうしていいか困っていたところ、山田さんが助けてくれた。
* While I was in trouble as my computer was not working, Yamada-san helped me. 「~いたところ」= While. 「~とき」よりも時間の間隔があるよね。When... is more “the moment”, “While” is a certain period of time.
広範囲にわたった海の汚染が、問題になっている。
* The pollution of seawater over a wide range results/turns in(to) a problem. 「広範囲に渡った/ 広範囲に広がった / 広範囲に及んだ」
立春は暦の上での春です。
* The first day of the spring is deem as a spring on a calender. 「暦の上での / 暦の上では」. In this case, 「~上で」 is “on”.
皆様のご希望に沿う結果が出るように努力いたします。
* I will try do my best shot in order to satisfy your hopes. 「結果に沿う(そう) / 結果に満足できるように」
そこは電気さえない山奥だ。
* It was a mountain without even electricity. 「電気さえ」= even electricity.
わたしにも言いたいことが山ほどある。
* I have many things to say. 「山ほど(たくさんの)」. So “たくさんの” is 省略されている.
言葉さえ共通なら、お互いにもっとコミュニケーションがよくできたでしょう。
* We could communicate with one another well, if we speak the common language. 「言葉さえ共通なら」= 「言葉だけでも共通であったとしたら」
ファンの人気投票をもとに審査し、今年の歌のベストテンが決まります。
* The top 10 songs of this year will be decided based on the popularity vote from fans. 「をもとに」is “based on”
ほしいだけ本が買えたらどんなにいいだろう。
* It would be great, if I could buy as many books as I want. = 「欲しいだけ(たくさんの)本」
考えるだけ考えたが結論は出なかった。
* I worked out as much as I could, any conclusion (idea) was came out. = 「考えられるだけたくさん。。。したが」
* Worked? I thought “to think” = 考える. Is it some idiomatical usage of verbs again, doing this Verb-presentだけ(same)Verb-past ?
木村さんのお父さんも学校の先生だとか伺いました。
* I heard Kimura-san’s father is also a school teacher. This means「先生だと伺いました」. But if she says 「先生だとか」 then it implies she is not sure yet if Kimura-san’s father is a teacher. (Cloud be a business man or sales guy.. so asking it politely.)
書く前に注意すべき点を説明します。
* I will explain what we should be care before writing. 「すべき」= should/ ought to.
木村さんのお父さんも学校の先生だとか伺いました。
* This is the same of the above.
もの
That one was a bit difficult to grasp.. I hope you can show in your translation the meaning. (It’s so ambiguous to me!)
あんな大事故にあって、よく助かったものだ。
* (Even thought) he/she was in such a big accident, it must be surprised that he/she was safe. In spite of being in a major accident, he/she was lucky because he/she is still alive. 「~もんだ」in this case the person surprises that he/she/the person itself is alive. But if a sentence is 「(昔はよく)~もんだ」then “I used to...”
いつか京都に行ってみたいものだ。
* I’m hoping to go to Kyoto someday. 「いつか~したいものだ」= I’m hoping to ...
時間のたつのは早いものですね。
* Times fly, isn’t it?! 「早いものですね」= You agree that it is fast / Isn’t it fast?!
地震のときは、だれでもあわてるものだ。
* Anyone would be panic during an earthquake. 「誰でも~するものだ」= Anyone would...
年末は、誰でも忙しいものだ。
* Everyone will be busy toward the end of a year. 「誰でも~ものだ」. It’s the same contract.
人の話はよく聞くものです。
* (It is said) You should listen to others well (carefully). 「人の話はよく聞くものです(よ)、(と昔からよく言いますよね)」It used to say for years that you should listen to others well.
人の陰口を言うものではありません。
* You shouldn’t talk behind someone’s back. 「人の陰口を言う(ことをする)ものではありません」
子供のころ、いたずらをして、よく父に叱られたものだ。
* I used to be scored by my father when I did mischief. 「(昔)~したものだ」: used to
この辺は、昔は静かだったものだ。
* It used to be quiet around this area. 「(昔は)~だったものだ」: used to