I prefer to bet rather than checking the flop. It does not matter your hand cannot stand heat, if villain is raising you are folding anyways. Combo hands where the draw-component is nutted fit much better into a calling range due to playability issues oop. The 99 pair makes the hand vulnerable, less improvable and the combination of top-pair made hand value and flushdraw value function as blockers to a possible call aswell. You want to make villain pay for his draws right now and protect your hand, deny showdown equity. If you hit the J-flush you might bluffcath 1 more street by x/c which gives your hand some playability especially against someone who plays as you have described.

On the turn you pick up another flushdraw-redraw. The top-pair, the 2 flushdraws and the gutshot all together give you are pretty strong hand. Beside this the J and the 99 are straightdraw-blockers now too. Because of all those components are working together you have always decent RvR-Equity and many good river cards aswell. For those reasons I would second-barrel the turn. As played the question on the turn is not wether to bet/f or x/c but rather if we bet/c or x/r/c. If villain is stabbing loose here, I would prefer to check-raise the turn.

I wouldn´t 3bet this holding here. It´s ok SB against a loose BTN opener. But here villain is isolating a limper. I assume his range is a lot stronger compared to a regular BTN steal. Besides that, the limper may call as well and this hand isn´t amazing in 3 way pots.
Not sure if you can call against 4bets as well. It´s probably marginally +EV given that it´s double suited but taking PLO10 rake into consideration I guess it´ll be close to break even.

Postflop I´m fine with your flop play, you won´t get much value here, you don´t have much to protect against and you´ll be able to call most of the turns so not a big deal. Turn I´d rather bet to charge weaker hands, he has a lot of weaker straight draws/pair+FD/straight draws+FD that you can get value from. If you have a read that this guy might overbluff here I´m ok with checking as well.