Hand 1:
I would just call the turn bet. 2 scenerios:

A) He has a bigger overpair. Here, you have 10 outs, so rely on them instead of trying to push him off of AA.

B) You are leading against AK. Here, he has 6 outs, so the only way to get anymore money out of this hand is to dodge one of them on the river. A minraise here though could bump him off of AK before the river. Although, you won't extract any more value from him after a possible river bluff attempt.