We don't say "may you" in English. We say "would you," or colloquially "can you"
Yes, "may I?" is correct, but not "may you?" as a question. As an answer, "you may," is correct
Yes, I guess you could say that. Not "formal", but "more formal" than without it.
The more Polish I learn, the more I realize that the Ukrainian language is just a version of Polish, only with Russian grammar. Ukrainian can also use "чи" ("czy") at the beginning of questions exactly the same as Polish uses it. Чи also means "or," just like Polish czy.
Russian does not have this at all.