As I look things over, a fold PF feels kind of tight, but a raise too loose. Should I be dancing with hands like this at all? I feel like the rest of the hand was correct, but feel free to offer other lines.

Considering you only have 60bb, you won't make as much if you flop a set. I don't like playing QQxx type hands in general (even if there are 100bb effective stacks), because you are likely to be raised PF and if you call, you're forced to play the hand OOP. If you are going to play these hands with the intention of flopping a set, I'd try and do it in later position so you'll have better position and you can just limp. I'm not calling with this hand in LP if someone raises pre. Also, even when you do flop a set, it'll sometimes be on a extremely wet board like this, where it is very likely that someone has a straight here.

As played, i fold the flop here. You aren't getting correct odds to go for a full house, and its going to be very hard to get payed against stronger (thinking) opponents, because really this is the only type of hand you could have on a board (2pair or a set, most likely a set) like this without having a straight.

Bet turn, otherwise wp.

I do not like the limp pre, if you are raised, it will be awkward. Overlimping would be fine. IMO fold or raise pre. if you raise you can flop a relatively hidden moster and have decent possibility to win the hand by just having the initiative.

I would bet the turn smallishly. Like $2 or so.