"emend" is not a common word. It's usually used about text. 99 times out of 100, "amend" is the word to use.
"evade" has a stronger sense of deception or of escaping from something. "evade answering the question" is not natural to me. I would say "evade the question". "avoid answering the question" is fine.
"admission" vs "admittance" ... can't think of much to say about this ex