You block Qh, which makes this hand aworse bluff catcher. I dont mind checking back OTF, taking freecards isnt that bad. I also dont mind 3betting the flop as it makes it almost impossible for villain to continue. OTT nothign really changes as villains range consists of Jx and hearts and I dont think villain triple barrels on this paired boards as you can simply bet /call down with all your Jx and better.

I'd jam a lot vs a 3b otf if I were villain fwiw

I'm peacefully folding otf, no reason to continue imo
xb otf is certainly feasible, cbet is also fine

Stack sizes also make this hand weird. Just fold flop, no reason to float there. He's favored w/pocket pairs, 2 live cards+FD, or any Jx hands. As played, I'd fold turn when he puts in half of his remaining stack. Yeah, you're getting good equity against FDs and pocket pairs now, but I don't think it's likely that he has a FD or pocket pair OTT. Plus, even if he has Axhh, then you're losing OTR like 25% of the time. Not a good spot to bluff catch bc you'll be right sometimes, but you end up losing a lot more I think.

I'd either bet full range really small otf or just XB - i don't see any point in betting so big here.
As played, I'd also just BF flop - we'll have enough hands to continue imo.

Once we call, defenitelly folding turn - this just looks like obv milking, and we have the Qh.