1. Fold pf. You're OOP and you really don't wanna be calling with AK even. That's just bleeding. If he's a real bad lag then 4bet AK is probably best. His turn bet size is sometimes a bluff. However, I doubt it is often in this pot. Probably played fine, though.

2. You have him beat most of the time.

3. Check flop. I'm very surprised you called his raise because it's obvious the only part of his range you beat are bluffs, and he has an ace a bit. Obviously he was a maniac. I'd rather call turn/river than bet/call flop. You check flop because you're wa/wb and cannot stand any action. It also looks to him like you flopped AAA.