The root УЧИТЬ, and its descendants

This tree of words is by far one of the hardest to fully memorize. Perfectives and imperfectives aside, the words all seem to have slightly different, large sets of rules and even more varying usage, and even share words at times. Here, I'd like to form a real, working list of all the words and their exact usages, as well as the structure of their verb arguments (meaning: how the subject, and different objects relate to the verb).

I've tried to start out with the easy ones for me to understand, but I'll definitely need input for the more complex words.
https://docs.google.com/spreadsheets...it?usp=sharing

(no other natural case uses) would mean that, for instance, Instrumental COULD be used, but that's just because it is a versatile case, not because it actually works into the word's core arguments. For example, I imagine, "Я изучаю русский язык книгою." is generally okay[ I assume ]. But my point is that книгою is especially extra, even more so than русский язык is. [one could say я изучаю and leave the sentence at that, correct me if I'm wrong] This distinction will help when we describe the words that can take dative, accusative, and or genitive objects all at once.

Quote:

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Originally Posted by xXHoax

For example, I imagine, "Я изучаю русский язык книгою." is generally okay[ I assume ].

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This particular sentence is not okay :)
You can say «Я изучаю русский язык по книге» but not «книгой/книгою».
In general, yes, the instrumental case works like you said.
E.g. you can say «Я учу стихотворение маленькими кусочками» etc.