I think the PF 3bet is fine given villain's highish fold to 3bet for heads up.

K92r with no BDFD is a flop that I would much rather check/fold since you have little to no equity when called and there are few to no good turn cards for your hand to improve on. It's also a board where villain should have a pair or GS a lot of the time meaning a flop cbet/turn check-fold is pretty bad.

As played on the flop, the turn is close but I lean towards a check/fold since, even though villain folds to cbets only 1/3 of the time in 3bet pots, most of his hands that weren't pure floats have no improved. The board could get much worse for your hand on the river and villain is very likely to barrel off with his occassional pure float give your line so you are almost committing your stack with the turn check/call.

My personal preference is to not 3b this particular hand at any significant frequency vs a 71% opener.  Nevertheless once done you have a profitable flop cbet vs his range on that board.  I think you have to c/f the turn.  

I think pf is fine.

I x/f flop since he's not folding much. As played you have to call turn, then eval river based on how you expect him to play Kx. Against a villain who bets Kx only once (either turn or riv), then I'm def x/c riv too, esp if he barrels off frequently when our range looks as capped as it does here. There just aren't enough value hands he can have that play this fast