Answer 1

Struggle wont work, unless your PP is all gone. All other moves will work.
If Mentronome or Assist is used, the move that the move uses is Sketched, for example, if Togepi used Mentronome that appeared with Signal Beam, Signal Beam would be Sketched, not Menronome or Assist.

Answer 2

Chatter and Struggle.
Some moves must fail in order to be Sketched