JJ vs. smal stack on Q turn card.

I think it's nicely played. Personally I check behind those rivers as I don't see what hands will call us for value. This may be a leak on my end though as I am trying to see how to do lighter value bets.
Maybe a better line is to make like a 1/3 - 1/2 bet on river.

Turn is a check for me,

I like it as played. Vs a bigger stack I would maybe bet the flop bigger. For me the turn bet is fine in order to protect vs. draws on a wet board.

Well played, you can push the turn basicly he will call with any pair or draw, if he has something like QT Qx flushdraw then life sucks (even then you have around 10% EQ)

Against a full stack player I think this line would be just fine. I would bet the turn in order to protect from draws and OTR I would check behind because I don't think many worse hands would call. However, in this case I think shoving the turn could be a decent option. As played you are leaving very little money behind and could face somewhat awkward situation if villain shoves OTR.