We should check call at least once here as there are a ton of draws and the Ace should not help improve to 2 pair but only a nut flush draw and a pair so villain reps that or sets.

Check calling turn would be normal. But it would still be thin. You opened UTG and c bet into multiple players, your line looks very strong.

It might be important to note that on the turn you are up against the CO who is much less likely to have a decent Qx as he overcalled, and would be expected to squeeze AQ KQ.

While it might be somewhat reasonable to x/c in a heads up setting, there is not so much of a great necessity to protect our checking range when multi-way. It's also a much bigger issue to give free cards to multiple opponents.

So usually betting for value/protection is good. If we feel it is going to be thin (especially on later streets), then it's fine for us to reduce our bet sizing to less than half pot. Even really small sizings will be ok here, and generally have a better expectation than a check. At least we can ensure the trash hands in our opponents ranges do not freeroll a turn.

For me this is a fold pre from UTG. It's pretty close but in general I'll fold this.

As played I would check the turn as we're not scared of too many cards and we probably won't get 3 streets from much worse.

On the turn I check call and then check fold the river. This could be a mistake though, but I feel like we have enough equity to call the turn especially when we check. he could easily be caling the flop with some draws and weaker Q's that would bet the turn when checked to.

I liekt he bet on the flop. You don't want to eb giving free cards away to two players! On the turn he can't have a worse queen and the ace does improve some of his flushes so c/f is probably correct.