1) I haven't worked through a NLH hand for a while but first off you need to figure out how your range is constructed in these positions, then take how many value combos you get to this river with and how many potential bluff combos you can have. I would usually choose all my back door flush combos + back door straight combos as a starting point because were going to cb this board at a V high frequency, if you triple all of those though your likely going to be heavily weighted towards bluffs when the board bricks out.

Your laying Villain almost 3 to 1 on a call so lets say you only have ~40 combos for value KQ-AA + flopped sets, villain only needs to find ~13 bluff combos to break even. You can figure out the best hands to barrel from that starting point, if you think you have way more bluffs that you want to arrive at this river with you can increase your sizing to reflect that.

2) Not the greatest of spots for villain to be bluff raising river without some kind of info on hero or some dynamics given that our value range should be pretty strong. If I felt the need to bluff raise here vs aggressive opponents I would be using some kind of hand that contained an A 8 or 2 blocker that we get to the river with and is now the very bottom of our range.

Quite a lazy reply and it may not be totally correct but hope it helped a little.

On a K82r it is hard to bet three streets with air as people are likely holding on with Kx 8x, maybe 99 77 type hands and some A3-5 with a backdoor flushdraw. To bet flop turn and river your value range should be Kx+ which is fairly narrow. Villain dependent they may decide to bluff all the hands listed. They may take 8x 77 99 A3-A5 and decide because your value range is fairly narrow it is a good spot to x/r river as a bluff. My experience is that people so rarely do this and they just have K6 or some such here.

You need to call $28 to win $111.5 so 1:3. Construct a range where he has bluffs or worse hands than you 25% of the time and see how it fits with how the hand played out. Likely folding is correct.

Very creative and ambitious if villain is bluffing here. Very unlikely since it looks like a value bet giving you a good price to hero call.
Do you have a history with villain? Are there any showdowns in similar situations? Whats villains playing style? Any HUD stats?

44, 55 are the obvious ones with blockers to 45 but it is unlikely villain gets to the river with those. A4s & A5s could certainly get to the river and block AK, 45,

Btw - is 100nl at natural8 that soft that you could get value from KJ/KT here?

@TheGoodTheBadandTheUgly BB got like 120 combos that will continue flop. If you don't call KJ/KT, how many combos out of those 120 will you end up calling with? You'll raise sets earlier streets.

Are you guys just calling the turn bet if you turn you BDFD with Ac5c? Or other bdfd?

If I was playing good I would checkraise the turn a lot with A4 / A5 cc (maybe A2cc). 2 combos there and 3 combos of 22 and 3 of 88 for balance. Most people though do check call to peel then they check call again. It requires a lot of poker background imo to be check calling those hands here and check raising turn.

If I had like KTcc I would not be check raising the turn.

If I had a read that you did not continue the turn light I might be check calling turn with 22 88 expecting you to bet river - if I thought your turn bets indicated a river bet would be coming and was made hand heavy.

All in all this could just be FPS and I would be check folding flop most of the time without some extended history with the player.