1. Yes.  On an input list with n integers, mergesort runs in
O(n lg n) = O(n^2) time.

Alternatively: If we sort a list of k integers, each in the
range 1..k, the input is n = k lg k bits long, and the running time
is O(k (lg k)^2) = O((k lg k)^2) = O(n^2).


2. Yes.  If A invokes B O(n^c) times, plus takes O(n^d) time, and
if B takes O(n^e) time, then the total running time is
  O(n^c n^e + n^d) = O(n^f) where f = max(c+e,d)
which is polynomial.