1) I probably bet the flop because you are likely to get some action most of the time I think. Checking is not that bad. I'm not sure about the river flold but yeah I guess he has a FH here more then he has AK.

2) Is there any 3betting history here? If not then it is pretty likely that he has either QQ or AA on the flop and I fold. I think this hand is very likely AA.

3) Looks ok. Your equity decreaces alot on a blank turn so just get it in now.