No checking turn is fine to then just check fold.

Played the hand well just don't bet so big on the river. Villain has made it clear he doesn't have much and this river hardly helps his range.

I like the line we took here. Don't see any reason to bet the turn, I'm basicly ready to give up there because even if we river a K or Q we're still in a pretty tough spot. Once we bink the river I think I'm going for a sizing like yours, but I think strato is correct that we're not getting calls that often.

I would say checking turn is standard. If you want to barrel on a blank turn such as this then it's because of a specific read that you can fire most rivers and expect to get enough folds.

As played I don't mind your size on the river. Villain can check behind turn to pot control with the intention to call any bet less than pot on the river. BvB you can still get called by Jx here more than enough imo

I think checking turn sucks here with nut-gutshot. We can't profitably x/c, and we'll be check/folding a hand that is possibly even the best hand and has nut potential. So I would 2-barrel here. Also fine to put some combos in flop x/c range with intention to bluff later streets where possible.

I would normally check the turn here but will bow to W34z3l's wisdom. I suppose we are immediately putting villain on an A but realistically villian's range is going to very wide and I am in the habit of floating tons of flops with all sorts of draws so any GSSd, FD even Pairs are probably not folding to the first bet when IP so barrelling is going to be profitable and we could still river a straight or a pair which will be god at showdown.