Hand 1: Given that Villian called the 3rd bet rather than pushed implies QQ/AK (or remotely JJ/TT/AQ) and he has about only $6 left (and there's $13 in the pot). Your choices are check or push. I can't see villian folding (except with the remote JJ/TT) could he fold AK? On that flop he might as it's likely you flopped a set. I say push because you are getting 3:1 on your money and there's a small chance he'll fold.

Hand 2: Fine as played

Hand 3: You have to call. I think villian is praying you have AK. The likelihood of him having JJ is offset by QQ/KK.