Steven, I wish this knowledge stayed as effortlessly as it came to me. I think by now I have lost a lot of my Hebrew conversation ability, but back in 1996 I could talk fluently. Practice makes perfect.
Indeed, French and English are cognates, and it should be noted that Japanese is a SOV language, English is an SVO language, and Russian (though SVO) allows a whole lot of word order recombinations. It's interesting that when I ponder some Russian words, it eventually hits me that it is actually a French word. Damn the 17th century aristocracy.
Yes, you are correct in your assumption. Just yesterday I was looking for the common word for "body shop" or "auto repair shop." jisho.org finally yielded 修繕工場 (damn the British-American differences, by the way). Sure enough, my Japanese friend has just told me that this is the wrong word to use. How would I know otherwise? Keep performing random Google searches?
I think you are also absolutely correct with regard to precise meaning. I actually never learned the grammar of the English language--that is, before I became an ESL/EFL teacher in Japan and later in Vancouver. The different senses and conditions you mention came to me naturally. Likewise, the あいづち you're talking about (by the way, laughably translated as "sounds given during a conversation to indicate comprehension; back-channeling") had bewildered me quite a bit too, at first. Now it just seems natural to intone a long ええ～！ in surprise, or a short え in agreement, etc. Context and body language...but, then again, that's just like the difference between word stress:
WHOM did you meet at the store?
Whom DID you meet at the store?
Whom did YOU meet at the store?
Whom did you MEET at the store?
Whom did you meet at THE store?
Whom did you meet at the STORE?
You get the idea.
Oh, yeah, and idioms for colours. This has always been a favourite with my students. In Japan, pink is the colour of エロ, but in the West pink is the colour of innocence and *blue* is the colour of sexuality (blue movie)...but then again, you could be feeling blue, or be green with envy, or seeing red. Good times.
Well, to answer your question, do keep in mind that I am an emigre. Having arrived in Canada when I was about fourteen, I became detached from a fully-immersive Russian-speaking environment, so my Russian is probably 85-90% "authentic" by the standards of a "native Russian." Having said that, I certainly see the problem with false cognates, false friends, and just plain dumb assumptions that, I think, describe something akin to your venn-diagram problem. For instance, revisiting some of my earliest poetry in English I found both awkward or totally inappropriate word usage or word usage that *could* fit the sentence--in general--but never in the specific context it was used. In this regard, I suppose I had to abandon English-Russian-English translation and go full force into English-English definitions (definitions of definitions), which is the natural step for all advanced learners.
...but let's make an objective study of this. I'm going to pick a word at random. Let's say..."anger."
The Oxford Beginner's Japanese Dictionary very helpfully states:
anger noun
= いかり・怒り
angry adjective
to get angry = おこる・怒る
to be angry with someone = だれかにおこっている・誰かに怒っている
There you go. No complicated conjugations, no part-of-speech confusion (because the sense in which I'm writing may pertain to the action, which would have to be formed from the adjective, unlike from the verb in English). You can just start building sentences!
Now, let's enter "anger" into jisho.org. The first word is はらだち, then どき...いかり comes up 19th! How would I have known to look there? They're *all* "anger"! Ah, but you say, click "Common words only"...well, it still comes third, and it is still the wrong word. On WWWJDIC, the word doesn't even come up on the first page.
Although I have almost outgrown it, I love the Oxford still, because it also has 35 pages of usage notes, 34 pages of the "Learning and Lifestyle Kit" and a grammar bit at the beginning. The editors at Oxford obviously knew what they were doing.
Finally, in answer to your question regarding the marvel of technology I have found on iTunes...allow me to tantalize you a bit:
Oh, I do wish it were $50 cheaper!