I'm pleased to say I got 88% on the first big test! I have a few questions however.

1(2) 東京から大阪まで車で一時間で行ける＿＿＿がない。The answer is わけ, meaning there is "no need too". But surely driving this distance in an hour is an impossibility! Is this the answer because the other choices -こと、もの、ほど make no sense?

1(6) 病人は悪くなる＿＿＿で回復の見込みはありません。The answer is 一方, but I choice せい. Don't both make sense in this context?

1(10) 長い考え＿＿＿計画ですから、失敗しても後悔はしません。The answer is ねいた, but I chose きった. Don't both mean "totally"?

Thanks for all your help everyone! I hope my frequent questions are more useful to others than they are a pain to some ^^

On my phone in class so I can't give a good analysis for you, but just something real quick.
わけがない -- I wouldn't use this to mean "no need to," especially with the potential form before it. It's kind of like "there's no way (reason) you could go ... in an hour"
I hear わけ(が)ない to mean "there's no way I could/would"
お前にプレゼントなんてあげるわけないだろ？
No way (reason for me to) I'd give you a present

I'll see if I can't get the others after class

病人は悪くなる＿せい＿で回復の見込みはありません。 would be odd since it sounds like "The patient's deteriorating condition is causing there to be no signs of recovery." You just wouldn't use せいで in this style of cause and effect. It's like saying "the sky is blue, which is causing the sky to not be red".

For the second one, ~きった implies doing something to the end, like reading a book to the last page. You can't really consider something "to the end".

Sorry, I still don't understand the difference between きった and ぬいた

Hmm, this one's a bit tricky. ぬいた is about going through something, especially something that's not much fun. 日本語文型事典 explains it as 「必要な行為・過程を全て最後までやり終えるという意味。苦しさに耐えてやり遂げるという意味合いが強い。」

きる has a number of meanings. First is 「「最後まで...する」「...し終える」という意味を表す」. Second is 「「十分に...する」「強く...する」」. Third is 「切断するという意味を表す。そこから、捨てる、あきらめるという意味にもなる。」 Fourth is the ~きれない form which means 「完全に...できない」. (That last is worth remembering as a special case, it's quite common.)

So 考えぬく would be to think through something completely, with the emphasis on the 'thinking through'. ~きる is more about having finished something, I think, so it doesn't really work with 考える. (I guess this is where the 'cutting' comes in -- it's over, done, you aren't doing it any more.)

Google threw up this page with some explanations of this exact KM question which looks good.

Thanks pm215- your answers are always brilliant. I'm glad too that I'm not asking (only) stupid questions - seems like other people have had confusion over the same questions as me.