I'd check-call the turn here. You really don't want to get raised here, but your hand is way too strong to fold.

KQ/QT/KT are all reasonable hands, and a lot of his range picks up straight draws on the turn, so most likely doesn't fold anything but maybe a weak Tx hand.

I think you can consider ch/c the flop with AK here. You're not likely to get a lot of folds with a cbet, you are going to get raised a bit on QT2hh, there's no great turns for you aside from a non heart Jack (even a K or A is tough, as we see).

bet 3 streets for value..fold to a raise.

I did c/c turn and I m not convinced by c/c flop. Tbh I think they are likely both suboptimal mostly because of how we are going compose our ranges. I dislike c/c turn enough that I think c/f turn is better. We can t call 2 streets worth of bets and when villain does bet his range is going to be pretty strong likely.

After playing around with some ranges we re going to have ~ 40-50% when called OTT and most of the hands that fold to a bet we dont really mind folding anyways. So I feel bet turn then c/f basically every river is going to be best. Maybe c/c if you have a read that villain is capable of some really thin value bets or is turning some idk TJs type hands into a bluff. Its a very complex spot though and the main problem is that this hand is just that awkward mid strength OOP that you wish we could just check down.

If Villain´s range on the flop is any mid pair+, flush draw and oesd (which is like 45% of his defense-range) he gets to the turn with enough hands that will call a 2nd barrel and bettting is superior to x/c. River will be tough, but most of his drawing hand have showdown value anyways, so unless he´s prone to turn JJ or QJs into a bluff it´s likely a x/f.