1) OK, villian may be a moron, but is he insane? He min-bet and you raised on two streets. On the river he min bets AGAIN. Insanity is doing the same thing over and over and expecting different results. The third time he min bets into you, you have to at least consider that you are responding in a way he likes.

2) is sick. There is a good chance that he thinks you are weak from turn action, and have to fold anything < A. At best he has AX where X is also a terrible kicker. I'm torn.... it looks kinda bluffy, but I guess it could be some wacky trap or A6-7-8.

3) not sure I can lay down T+B here... but really all you beat is a bluff. TXd or QXd? But wouldn't they just call river?

4) PF is meh, unless you have been 3-betting light. You are in position, so I grant calling here isn't terrible. Since you are now crushing AK, I guess you have to keep going? I think I would just rather fold PF.