[nietzreznor]

Hand 1: Don't think I like the flop minraise here. Problem is, you scare villain with your raise, but you don't get a whole lot more money in the pot. I'm tempted to just call here, and raise the turn.

Hand 2: Well, I guess the short answer here is that if you think he has Ax, you bet as much as you think he will call. This is pretty read dependent. As you played it, I might bet a little less here, since your turn minraise may have scared him a bit.
As for the turn minraise, I think you should either flat call or raise a bit more (your raise here is only a 1/4 pot raise, I think maybe 1/2 pot here would be better). If you think he has a worse ace, there probably is no harm in just calling here and getting another bet on river. Though if he's loose, I could definitely see him calling a 1/2 pot turn raise, and a 1/2 pot river bet or so with AJ/AQ.