1) I'd bet entire pot on the river ($0.20?). He's probably not calling with a busted FD, and I doubt he would turn it into a bluff. I think he would call with an ace, but I'm not sure.

2) I would probably 3 bet 3.5 to $0.20, as played bet about $0.30 on flop, as played call the raise because of how much your hand looks like AK.

3) Why is the raise so big? What are you trying to accomplish?