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* perfective is used in such requests when you wish a certain result
** However, "можно помочь" sounds either detached or "can it be helped", in a pessimistic way (what you are likely to ask your...

The basic meaning is
вычистить : clean out (entirely/diligently/took long etc.)
подчистить: clean up a bit, or clean a few spots (on an otherwise clean object) that have become dirty.

There is always some difference. "Проснуться" is more common in ordinary life. However, each time you encounter words with similar meaning, the context may slightly differ, or one can be older, or...

"-ка" is a particle, its meaning and use difficult to formalize. Here it makes the imperative more emotional and urgent.
-ка - Wiktionary

Just use "понять": it is more widely used. "Постичь" is the same as "undersand", only more bookish and implies a deeper degree of comprehension: full understanding, getting to the essense of things. ...

That's wrong. These are two verbs, пить is imperfective, выпить is perfective. Also, выпить may have a slighltly stronger connotations that the drink may very well be alcohol.