Villain (BTN) is a nonreg player, it is clear that he is quite clueless. He plays too many hands, like any two suited etc', he loves to make rediculous overbets (like 80 into 20 pot), as well as huge check raises with the goods. He happened to run extremely good, turning 200 into over 3.5k by making monsters redic number of times. He is not aware of position and pot size. Overall, he seems to be passive and I didn't see him bluff but he visiblt gets excited of all the chips in front of him and I think he opens up his game. So far, I instamucked to his check raises at least 2-3 times when I was c betting in position.
Hero has 1700, BTN covers
Hand:
3 callers,
hero raises to 35 w TdTh in SB,
BB folds, 3 calls
Flop (140): 2dQd2s, hero bets 90, only BTN calls
Turn (320): 2c
Plan from here?

I would likely b/f because you said he was passive. Small % of the time he might raise with a smaller PP but Id think you can still get value from overcard/flush draws if hes terrible. You said when he raises he has the goods so seems like a easy bet fold.

I also don't mind checking turn and leading river for half pot or c/c depending on the river.

How do you think he would play a queen?

How much is the bet, also what do we do on various rivers if he just calls? Bluff catch? Check fold? Block bet?
I think he just calls most of his Queens OTF and not necessarily raise them OTT. I expect he doesn't raise most of his worse pps pre and does raise JJ+. So his range OTF looks like any suited Q, Q9o, 33-99, some diamond draws.

I would bet about $100-150 depending on what can keep his worst hands in OTT. If the flush completes I will likely bet $150-200 OTR. I will c/f c/c depending on the bet sizing and my reads, too hard to say. The smaller the card the better just in case he can bink with his Kxdd, Axdd, Jxss. If the flush does not complete I will just c/c c/f leaning more toward a c/f since this villain should just be playing their hand as is. Unless villain wants to polarize with his be then it'll come down to your read again.

Board: Qd 2d 2s
Dead:

equity win tie pots won pots tied
Hand 0: 62.558% 62.04% 00.52% 104406 878.50 { TdTh }
Hand 1: 37.442% 36.92% 00.52% 62137 878.50 { TT-33, A9s-A3s, K3s+, Q3s+, J9s+, T8s+, 98s, Q9o+ }

If we can discount the 2 from his range (which we shouldn't be but I just go with the range assessment you gave me in your last post), our hand is not looking too bad. Idk what kind of suited range you give him so I just gave him connecters and some of the better gappers. All suited Kx and Ax suited too. And then the range you gave him on the flop.