yeah dont bet. you dont rep anything. and this 2 is a brick for both players. villains range consists of missed FDs (which you already beat) and medium hands he will not fold with this river. after his raise wouldnt be surprised to see villain turn over 22s here.

just c/f this river imo (against a pot sized bet you might bluff catch)

I dont bet this flop either fwiw. You are bluffing with very few outs. If there were two diamonds on the board I could make a case for it.

I'm quite hesitant about saying this sort of thing about a play in isolation - you have to work out what you're overall strategy is and work from there.

I would say not Cbetting this flop is OK but in that case you're going to have to not CBet some of your Ax hands and incorporate that as part of a general strategy where you don't Cbet much OOP. You'll probably also want to keep some hands to have as part of a x/r range e.g. a couple of nutted hands for value and some strong draws.

If your general strategy is to CBet most of the time, I think betting on relatively dry A-high flop is almost mandatory, it sucks just to check/fold every time we don't have an A on an A-high flop.

this board is better for our range then for villains. So i would def cbet this board at a high freq. KJ with a backdoor straightdoor is fine imo (preferred a heart in our hand ofcourse)

Flop should be a bet. It's true that a lot of what we fold out is things we beat already, but those hands have 25% against us and we can't just sit around waiting to bluff-catch over 3 streets so it's almost irrelevant we have showdown value. Occasionally he will also call with a weaker K high then check to showdown so we do get value. It's hard to think about this bet because it doesn't easily classify as value bet or a bluff or even a semi-bluff. It's one of the "Chess" situations where it's just a better line than any other.

On the river we do still beat some of his hands and have plenty of other potential bluffs so I'd check this (mostly check-fold but you can call a smaller bet) and see if we're good.