from lesson 9:
"Ga shows phenomenon.The particle ga may describe the existince of a non-specific thing. However, the particle wa, as we will see next lesson, is specific and known by the listener and speaker. "
Where did you read this? Your example 波が高い could in another context be 波は高い. It's still showing a phenomenon. 雪が降る could also be 雪は降る. Notions of natural/unnatural, new/old information, emphasis/forcefulness that you mention on your site aren't at all necessary things to consider when you speak. It's much simpler than that. You simply use が to specify grammatical subject for clarity or for identification within a sentence or clause, and は to clarify/change what you're commenting about. It's really that simple. You could start a novel with トム君は... The reader knows nothing about Tom at this point but will read on to find out. The writer is simply using は to basically show now I'm talking about some guy Tom.
Your examples:
犬が犬だから、吠える。
子供が子供だから、ごたごたを起こす。
are simply connecting two clauses with the word から.
They are not examples of your 今が今 and 皆が皆 (which should be mina ga mina btw) grammar point. Note how 犬が犬だ is a valid sentence (dogs are(だ) dogs), but 今が今/皆が皆 are not, they're idiomatic (hence they pop up in dictionaries.
from lesson 10:
"The particle wa shows emphasis,"
where do you get this from? This is not a generally applicable rule but rather something that may be true depending on certain contexts. What exactly does は emphasize?
"As you will see, it may single out an item and or distinguish it from other things, thereby emphasizing them. "
Actually が is more likely to do that. は simply specifies what is being commented about. The comment may or may not be specific only to the は marked word.
"Most sentences in Japanese start off with a topic."
this is not true. Conversations might tend to start with a topic. maybe. But If the topic is raised repeatedly without it changing, it sounds odd in Japanese, kind of equivalent to not using pronouns in English (he, she, it etc).
"The particle wa may describe an eternal truth, something that is know as a fact. "
wut? Didn't you say before that が is used for stating facts (also untrue).
"The particle wa can show existence, and it can also stress a degree. "
what does stress a degree mean? also I'm pretty sure verbs are used for showing existence in Japanese...
there are still some oddities in your example sentences, but I won't go over them now.