I'd 3b to 3x oop this deep and probably barrel off. Checking (also is ok to keep your checking range stronger) may increase the EV when his bet vs missed cbet is very high but there is no reason to x/s river if he is folding his one pair hands and calling 2p+.

Sorry I misread the action. Flatting AA is perfectly fine since your 4betting range this early should be too strong. I'd call down.

I'd have played the same way you did until the river. Villain 3betting and triple-barrelling in this blind level shows a lot of strength. Normally I see he doing this with hands like AJ+ and pocket pairs. But when he triple barrels in this dry board I'm concerned he might have a set, so I only call the river. Probably the only hand that will call your shove and is behind is AK, or maybe KQ if he is agro enough to 3bet it in early game.

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