1) I can see where you're coming from, and I think it's pretty close, but I prolly fold. What do you put him on? I'm finding putting him on a range fairly difficult here.
2) Mash the call/AI button really really really quick - even against the extreme worst case scenario where he's got 9hTh you've still got 30% equity.
3) I prolly check behind. If it gets there, I bet it (if he checks) and fold to a shove. If it misses, I prolly check behind or fold for more than 1/3 pot or so.
4) IMO this spot is made disgusting by the fact that you didn't threebet preflop. I prolly fold and feel really horrible about it.