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Well, I'm a noob, so I'm qualified to comment 
Pre-flop - 100% agree with call, but not much information available - you're paying for the chance of a set. Due to his pseudo-isolate move I consider his range most likely a 99+ or any two broadways. Suited connectors and lower pocket pairs I'd think he'd limp if he played them. I don't want to top-limit his range - I could see AA or KK played this way by someone worried if he'll get any money out of it (at this level).
Post-flop - he's min betting $0.04 into a four-way $0.38 (minus rake) pot. For the purpose of my action I'd think of it as him having checked - except I consider his play indicative that he'll call any raise that doesn't cause his alarm bells to go off too badly - he wants to play his hand and may even be scared of pushing people away so he won't get paid for it. I think his range is unchanged here - bets are too small to mean anything. Even AA could be played this way if he's worried about scaring people off.
I'd want to put in a healthy $0.3-$0.4. Calling is the equivalent of attempting a check-raise - a min-raise to some people at this level still looks a raise and they might not do the re-raise they otherwise would, but with people calling to get in on the flop and a four-way pot I wouldn't expect much aggression from them and would just go for the mentioned bet.
As played, when he re-raises to $0.12 he's obviously fond of his hand and thinks that he underbet it the first time and isn't getting paid off. At this point I would call. If you raise him at this point he'll be counting the number of raises rather than the amounts being bet and a raise from you would make him call and cautious later in the hand. Stacks will be less likely if you re-raise him at this point unless he draws to a full house or quads on the river - which beats you. While I agree an all-in on the flop would be nice, I consider it unlikely once it has developed to this point.
As played, on the turn the pot is three-way at $0.74, he's happy with the turn and worried about being paid off on his good hand and does a pot-sized bet OOP. His range now has any hand with a J (orT) removed if it doesn't also have a Q - rest is still possible: AQ, AK, KQ, QJ(s?), QT(s?) 99+. Ok, so I'm not confident about this bet if holding 99, TT or JJ, nor with the idea of him playing QJ (s or no) or QT (s or no) pre-flop the way he did. At this point you're ahead of everything except QQ.
I'd reraise him at this point - probably $2.5-$3 raise. It'll make him pause and if you take it down it's not the end of the world. If he continues to be happy with his hand in the face of that raise he has to consider that you're willing to play for stacks. He'd fold the lower pairs and AK, but hold onto AQ, KQ and probably re-raise you all in with any of those. If he'd played AA, KK, QJ, QT this way he'd probably call them.
On the river - many hands with a Q in them are firmly in his range (so his quad beats your house), as are AA and KK (so his house beats yours) - the only hand in his range that you beat is AK, and his turn-bet doesn't really chime with AK to me.
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