Hey! Beginner here, trying to improve from my worst hands.

Interested what y'all make of my play + bet sizing on the turn. And what you'd do on the river. Thanks!

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No Limit Hold'em $0.01/$0.02
PokerStars
4 players

Stacks:
UTG - UTG ($2.82)
BTN - BTN ($2.05)
SB - SB ($2.18)
BB - Hero ($3.34)

Preflop: ($0.03, 4 players) Hero is BB with Q 9
1 fold, BTN raises to $0.06, SB calls $0.05, Hero calls $0.04

Flop: Q 2 5 ($0.18, 3 players)
SB bets $0.09, Hero calls $0.09, 1 fold

Turn: 9 ($0.36, 2 players)
SB bets $0.18, Hero raises to $0.54, SB calls $0.36

River: K ($1.44, 2 players)
SB bets $1.49 (all-in), Hero ???

Some random 2 pair is probably as likely as the flush. No 3bet pre lessens the likelihood of AQ, QQ and maybe KQs, and you have a heart blocker. JT probably doesn't donk flop, unless JThh.
Think there may be enough Q2, Q5 and busted clubs for a call, reads would help here a lot.
I'm wanting to fold but prob calling here in a vacuum and making a note either way. Not sure if population is bluffing here at 2NL though.
Fold if SB has been tight and not bluffing, call if he's shown bluffs or light value I guess.

Villain stats:
VPIP 21 / PFR 6 (over 70 hands)

No 3bet pre lessens the likelihood of AQ, QQ and maybe KQs, and you have a heart blocker. JT probably doesn't donk flop, unless JThh.
Useful to see your thinking about their ranges.
Honestly hadn't thought about the lack of 3bet pre-flop ruling out QQ+. Thanks for that!

I'm wanting to fold but prob calling here in a vacuum and making a note either way. Not sure if population is bluffing here at 2NL though.
Fold if SB has been tight and not bluffing, call if he's shown bluffs or light value I guess.
Given the stats I just posted, I guess a fold is probably best here. I had no particular reads that they bluffed lots.

Question: how would you evaluate my $0.54 raise on the turn?
Should I have gone all-in on the turn?
Reasoning that 2pair is decent at the turn, and we want to deny the Villain the chance of a flush draw on the river. So making them pay a huge price to see it feels like a good play to me.

As we've ruled out overpairs, feels like the flush draw is the main worry here for us.

I'd go a bit bigger with the turn raise, maybe $.65 or even $.70. No need to shove though. If he has a flush draw, he only has 7 outs. You have the 9 of hearts, which wouldn't help him anyway if it were available, and the queen of hearts also is no good. So you want to raise enough that a flush draw is making a mistake to call, but you still want him to call.

Why are you betting? What ranges are you assigning your opponent?
Folding out Q2 or TT here is a disaster. If you shove, what calls?
River bluffs are rare at NL2, so if you are disciplined enough to fold rivers then pot or 3/4 pot is enough to price out the flush draws immediate odds. Here, nothing better is folding. If you make it too expensive, lots of worse hands that can call a value bet on the river will fold. That would be bad.

I would like to see a larger raise ott. Folding river to a relatively passive villain seems disciplined and pretty good. Flushes, JT, and KQ are all hands villain could plausibly have that improve to beat us, and I don't think a 21/6 villain is likely to get out of line with bluffs here (though vs some villains we should be considering the call).

Also, this hand is a clear preflop fold. It would be ok (pretty close?) vs just btn 3x, but going multiway with an offsuit disconnected hand that doesn't even flop strong top pairs is definitely not good. Defending bb too wide multiway with offsuit hands is a common mistake. If you have hands that seem close preflop, it's a good rule of thumb to just muck them and play a tighter multiway range, especially with offsuit hands.

Flop: Too loose. I only call here if I know my opponents are bad.

Flop: Good.

Turn: I like this size or a tad bigger. Much more though and it's too likely villain folds all the hands you are ahead of.

River: Fold. You beat nothing but a bluff. Is he turning Qx into a bluff? That's a play even good players probably don't make enough.

Haven't read responses ...

I think turn raise is a little small. You're giving him 3 to 1. And about pot size left. Going a little bigger might be a bit awkward. Honestly, I'm considering just shoving turn, if you might do it with some draws also. Or, practically, maybe just go a bit bigger here.

As played, I think river is an easy fold. Painful, but easy. He has a flush a lot. He also very plausibly could have KQ or JT. There aren't many hands he could have that you beat.