Mixed up on the turn

[DanK]

Ok, here is a hand I played recently and am not sure if I played it right on the turn or the river.

Loose bad UTG limps, unkown middle player limpa, I raise on the button with Ad jc, sb folds, bb calls, the 2 limpers call.

Flop: Kh 9c 2d

All check to me, I bet.
BB calls, middle player calls

Turn: Kh 9c 7d [Jh]

all check to me again and I bet, bb ckeck raises, middle player calls!. I call planning to call down (OK?)

This seems, bad, in retrospect I think I should have folded or three bet to take a free showdown unless I cought 2 pair or trips (and the flush not showing up at the same time).

River: Kh 9c 7d Jh [5h]

do I call if the bb bets and middle player folds?
If you get checked too is this a value bet on the end (I don't think so but is it even close?)

[Fianchetto]

Preflop: Fine

Flop: Standard

Turn: If the pot were heads up it would be a tougher laydown, but with a 3 handed pot like this the big blind is not likely to be bluffing, I would lay this down.

If the big blind has a set or a straight you are drawing dead, if he has two pair you can catch up, but you don't know which card you want, a jack may give him a full house if he's holding something like KJ or J9. Even if he is getting frisky with just a king, you are still behind, it appears you have the odds to draw but an ace may not be good if he called your raise with AK. This is where knowing your opponents is helpful too, if I knew the BB to be a weak/non-thinking player, I would lay this down without hesitation, if he can be tricky, then I probably still lay it down, since he is less likely to be pulling a move with the third player in there.

Also what does the third player have? He called the flop, called two cold on the expensive street... a pair that picked up a heart draw? Maybe he already has a hand like two pair, if he's not on a draw he's sure to have you beat.

River: Well, I probably would not have made it this far but you didn't improve and the flush came in so I'm probably folding to a bet and a call, if BB bets and MP folds, you are in a situation that I hate being in: You know you will probably lose, but the pot is big enough that you should probably call getting about 12:1.
If its checked to you I would take a free showdown, I mean he is not folding a better hand at this point, and I don't see what he would play this way that you are beating.