So if there are 2 possible animation targets in graveyards, one of which is a dragon, can I force a draw by targetting my dragon every single time?
No. You have to pick a number and break the loop.
If I go into a loop and say that I want to repeat it 100 times, and come out with 200 mana, can my opponent say that he's going to respond to something halfway through the 99th loop?
He certainly can interrupt your loop whenever he likes.