I would probably cbet 40%-50% pot here trying to fold out pocket pairs and face card hands. The ace hits your range harder than his. If you're not comfortable with a bet, I would check/fold and not check/call because we'd just be giving a chance for those face card type hands to hit. I'm not barreling often... maybe on a K or Q, to put a hand like A8 or AT in a tough spot.

I think you can check here as long as you balance your checks with AK AQ. I dont think he has very many Aces here mabye AT and some suited Ax. I think checking and betting is fine. If u check bet some good turns. i feel checking is the best here not 100% sure though. his range is probably full off QJ , KT, QT, JT and small pairs. i would check the flop and bet some small turn cards then if called probably give up and try to get to showdown vs maybe some smaller pairs.

I believe cbet here is more profitable than checking, as you still have some equity against the CO calling range, which is full of broadways. Board is quite dry although there is a flush draw. You'll get a lot of folds here.
Besides,you will have a hard time realizing your equity by check calling

yea also true. i think cbetting cant really be wrong here.

Seems a check is best. What parts of villains range can you get three streets of value from that you couldn't get all in with on later streets for 54bb. Checking also let's villan catch up slightly or bluff turns.

I woulld almost certainly cbet here.

c-betting seems best to make all his broadways fold