BEST MOVE

It would be nice to know suits of the cards. Pre flop you should play tight when you are UTG and face a 3bet. AQo is often a 4bet bluff for me but AQs is a call.

Flop can go either way. I think both betting and checking are reasonable.

I agree with the previous comment about the preflop part, AQs you can call, AQo maybe 4-bet but rather fold most of the time. I don't know Villain but his average checking range should contain AK-AQ and probably some underpairs 99-88. For this reason I would definitely bet the flop, somewhere between 50-67% of the pot. Although an average NL2 player is not likely to instantly lay down any of the above mentioned hands, you can fire again on the turn if it likely doesn't help his range. If he is known to slowplay his strong hands you have to be careful though, since he could have top or middle set. I don't know if there was a flush draw on the flop, but if there was, he probably isn't going to check call these hands on such a wet flop. If your flop bet gets raised it is obviously time to give up.

Yes, you can float the guy