Preflop
I could see this being a fold or a call. I tend to follow the advice and ranges that Ed Miller gives in
The Course, and QTs is at the bottom of his recommended range for calling a loose open from the CO.
As for whether or not Villain is loose, the PFR and 3bet percentages indicate that he's loose, but the sample size is small. Still though, most people at NL2 just don't 3bet nearly enough so if this guy is 3betting light, I'd take that as a reasonably strong sign that he's an active player. I'd also look for signs of fishy play, like limping and donking. If Villain was making those sorts of plays, I'd start to think that the PFR and 3bet percentages could be anomalies, and that maybe he isn't so active after all.
An important question to answer is how you're going to make money postflop. It'd be great if you had a read on Villain where you could bluff him off of some spots postflop. Eg. maybe Villain cbets everything and then check-folds the turn, in which case you could make money by floating. Another possibility is that you make money with implied odds if Villain spews, or if there are fish behind who give you better implied odds. If you have clear answers to these sorts of questions, I'd be content with a call. But if you are just "calling to call", I'd recommend against it.
Flop
Interesting spot. Versus a passive opponent, I would think they'd only be betting stuff that crushes you. It's hard to see a passive opponent betting AA, AK, AQ, JJ on this super scary board versus three opponents, especially when the bet size is bigger. Your opponent seems to be more aggressive though, and at NL2 perhaps people don't realize that AA becomes a pretty mediocre hand on this board. Still, even if they're betting some of that stuff, there's also a lot of value that they could have, and that either of the two blinds could be checking, so I lean towards folding.
Turn
When Villain bets a second time, maybe he could still have AA and AK, but I have a much harder time believing that he has something like AQ or JJ. It's nice that the blinds aren't in the pot anymore because now you don't have to worry about them slow playing the nuts, but I think that Villain's range is just too strong here to justify calling when you only have four outs.
By raising, I don't think that it accomplishes anything. If the raise is for value, Villain might be folding AA and AK on this scary board, and even if they do call with those hands, I think that they have enough value where you don't have the required 50% equity versus their calling range. If the raise is as a bluff, I just don't think Villain is ever folding something like KQ or TT at NL2. Check out the writing on
Fancy Play Syndrome. It's a trap that many people including myself fall into, and it seems to be what is going on here with the raise.
When Villain shoves over your raise, I definitely think you have to fold. It's even less likely that they have AA or AK now. They probably are only shoving with stuff that crushes you.