Most of the ones you answered are correct.
"Loosen up"/"limber off" do not mean to warm oneself up. In fact, I do not recognise "limber off".
"Spring up" is a sudden and/or unexpected appearance; it does not fit with "turn up" or "show up" (which are correct answers to that question).
As for the ones you couldn't answer, I looked up them up, and 9 might be "catch on" or "get it", but one could also say "it hit me", and 13 as a phrasal verb would be "play at". I don't know off the top of my head a phrasal verb equivalent for number 12.
[Not a teacher]