Turn decission

I would bet flop a little higher. As this Board hits BBs Range quite good. He has a lot of 5x,6x and backdoor draws/OESDs and you want him to fold his low pairs
Imo. Its hard to give SB a reasonable Range here. His overall 3bet is 15%. Its not a big sample, but its a tendency that hes 3betting quite some hands.

I think he has on the flop lots of FDs, maybe 55 and 66 and maybe some 78?
The Ad in general blocks his semi-bluffing Range OTF, so his raise has imo. more value hands. So you should be a little more careful.

OTR the value bet is close. As he most likely has some sort of missed draw or strong made hand, so villian is really polarized OTR. He maybe has some QdXd with a medium/bad kicker there. Your bet looks really strong right here and Im not sure if hes calling his Qx. I wouldnt size that big OTR. Maybe 1/3-1/2 pot.

I would just check back OTF. Pot is 3way where You dont have vbet and bluffing with AdQx here vs 2 people is I think bad as with 30% PSB You dont have enough FEq. Another thing is that You are not afraid if turn completes Flush as You have nuts redraw.
I bet that when he ch/r that flop vs 2 people he have much more value hands (both Jx for protection and 2pr+ for max value) than draws ( especially when You have Ad)

I would check behind the flop as well and if you Cbet you need to give up if you face a raise. As played calling turn is fine for sure. He has now 79,1bb behind and if you would raise you need to shove and I don't think you will get action of worse if you would do that. On river a bet of like 26bb is big enough for value I think. I expect he will fold a lot if you would bet more and even if you bet smaller the change he will call isn't to high with a missed draw He could have.

Cheers,
SDK1987

The small raise OTF may have been interpreted as a sign of weekness, so maybe the villain was just trying to steal the pot.
Btw i would check behind OTF and OTR

Given the small size, cbet is fine, if the plan is to barrel any diamond, or BW card. Turn ok. However, why do you bet the River? What do you expect calls from?