So i have a few questions about this hand.

Should i have raised preflop?
Should i have folded the river?

PokerStars - $0.44+$0.06|25/50 NL - Holdem - 7 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

UTG+1: 25.5 BB (VPIP: 76.47, PFR: 18.75, 3Bet Preflop: 0.00, Hands: 18)
MP: 34.3 BB (VPIP: 33.33, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 18)
CO: 71.6 BB (VPIP: 44.44, PFR: 5.88, 3Bet Preflop: 0.00, Hands: 18)
BTN: 23.2 BB (VPIP: 11.11, PFR: 5.56, 3Bet Preflop: 0.00, Hands: 18)
Hero (SB): 64.2 BB
BB: 3.1 BB (VPIP: 15.27, PFR: 12.70, 3Bet Preflop: 13.21, Hands: 214)
UTG: 48.1 BB (VPIP: 27.78, PFR: 22.22, 3Bet Preflop: 40.00, Hands: 18)

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 3h 3d
fold, fold, MP calls 1 BB, fold, BTN calls 1 BB, Hero calls 0.5 BB, BB checks

Flop : (4 BB, 4 players) 3s Js 4s
Hero checks, BB checks, MP checks, BTN bets 1 BB, Hero calls 1 BB, fold, fold

Turn : (6 BB, 2 players) Tc
Hero checks, BTN bets 2 BB, Hero calls 2 BB

River : (10 BB, 2 players) Ad
Hero checks, BTN bets 5 BB, Hero calls 5 BB

You're asking mediocre questions. The biggest error is not betting the flop.

You can't be so passive, you'll never win.

So would you raise, or check and then re-raise?

I'd be betting. Can you deduce why?

I'm a noob, and my post flop play is terrible, but I saw this thread and your question really intrigued me. I want to take a stab at the answer. Any chance you could tell me if I'm on the right track, or completely off?

There's a few reasons for betting that I can come up with:
-To get value from top pair/over pairs/two-pairs (basically worse hands)
-To get value from flush draws (or to make flush draws fold?)

Any help is greatly appreciated

See you do know it! Not as bad as you think.
Betting here is a must, giving a free card on that board would be a disaster for your hand. The purpose is to bet enough so that any worse hands by calling would be making a mistake if they knew your exact holding. A villain fold isn't a disaster as it could turn out to be a high variance hand. But even if they call, without a higher set or made flush they are making a mistake and you gain value.

Preflop seems fine, you're out of position against multiple limpers with a so-so hand and you're getting in cheap. And no, I would not fold the river here as played- villain has been probe betting you all the way. Obviously he could have the flush and be trying to keep you in... or he could have a hand and be poking you to see if you'll raise. By the river, he's probably feeling safe with 2 pair. I'm guessing a lot of people would even raise here, I would most likely call as a shove would make me sick and I'd be happy to win a 20bb pot in this spot.

Everything said here so far seems pretty spot-on. The biggest problem here is definitely the flop. Against 3 others with such a wet board you need to be betting out. I agree it's not a disaster if they fold, it's disappointing maybe but you cannot afford to give a free card here against possible multiple flush draws/straight draw, even 2 pair is basically drawing against us. (On a dryer board against multiples, you could consider checking with a set to trap, but certainly not here.) If they do have the flush, we still have outs after the flop.

It'd be great if we always flopped sets on nice, dry boards, but that's not how it works out. You don't hit that many sets, so get some value out of it when you do. Making the most out of tricky situations is what will set you apart from mediocre players, anyone can win with 333 on a dry board.

Again, I'm still learning as well, but I hope that helps. Good luck, and sorry for the essay

Another mistake is that you're almost paying 15% rake!

Pre fine, def bet flop ~4bb or even bigger. Jx not going anywhere and probably ppl call any medium/high spade as well regardless of betsizing.

Pretty irrelevant, 0.5$ SnGs are either played for pure fun or to learn the game, not for making money.