It's obviously hard to say without any info regarding to player tendencies, table dynamics, and game flow. That being said, I think your sizing on the turn is probably fine. It could be bigger for sure, but if you're worried that it was so small that it possibly looked weak and played a role in him raising you, I don't think that's an issue.

I think we are definitely too strong to be folding the turn, although if you were fairly confident he would be shoving the river a good percentage of the time and don't want to find yourself in an even tougher spot, then I suppose you could fold.

On the river is tough for sure. But realistically hes should be defending his BB really wide, and there are lots of different 2 pair combos and sets that absolutely make sense there, as well as some straights. I think if the river paired the board I would feel a bit better about calling. If he had a set or two pair, you were beat anyways so a boat doesn't matter, so at least it counterfeits a bunch of the two pair combos looking to stack a strong overpair.

He could definitely have some of those bluff hands you mentioned. So you need to decide if you think your villain has it in him to turn a pair and a draw into a bluff in that spot, or is he more likely to check and rely on showdown value.

Its a great spot for him to bluff for sure, but all in all I think you're beat here enough of the time that folding is the right move

You definetelly have to bet bigger ott, no reason at all to decrease sizing and go for a 1/3 pot bet. Bet around 2/3 - 3/4 pot to properly extract vs all his draws and pair + draws. Bet/calling is fine if you think vilain will bluff pair+draw type hands, otherwise just bet/fold.

Another option is to check turn, this will avoid the x/r and to be put in a hard spot.