Since I want to focus a bit more on studying, I'd like to check what I did here.

Pre - Standard

Flop - Villain's range should be heavily leaning towards small to medium pocket pairs and some broadway combo's that didn't hid (but might be drawing). I think a c-bet oop is the best option. (To get value from 66, 88 and flush draws) There aren't many straight draws in his range because I have two jacks.

Turn - In hindsight I think betting twice isn't the best. His range on the turn would be something like 4's, 6's, 7's, 8's, JT, ATh, AJh. I don't think I can profitable value bet this. My thought process during the hand was: there are draws possible, I need to bet. Not thinking a bit harder about his range was the mistake I made imo. (Would love to hear if you agree or disagree!)

Turn after the bet - As played I think this is a fold. Turn min-raises are very often very strong, especially on this board I think.

Thank in advance!

I think the turn bet is fine.
If you don't bet you'll be missing value from draws that haven't hit and giving them a free card.

When MP1 raises you're probably done with the hand, looks like he hit his straight there. Or maybe a set or two pair, you're still beat.

Although you are getting 1:4.47 to call (not sure if this is correct tbh ...)
There's 1.88 in the pot and it's 0.42 to call.

You have 4 maybe 6 outs and a small chance your hand is already good.
Still think it's a fold :P

Since you haven't provided any details about the villain I'm just going to have to assume he's a standard 2nl player. In this case I think you played the hand just fine. Betting the turn can pick up value from the flush draws as well as A-9/7/4, K-9/7, 10-10/9/8, 6-7/6. I think the range that you're describing is far too narrow. Once he raises I think you can fold (unless you have evidence of him doing this sort of thing in the past with air).

This is a pretty wet board so I could see the villain making this raise with many draws or top pair and a draw, etc. If he had a set or a straight I think he'd raise more to protect his hand. I think you should call here on the turn unless you have a read that the player only bets the nuts.