PREFLOP: You should fold, J9s does not play well in a loose aggressive game. Most of the time you will flop a weak draw, and youll never get a chance to see the turn in this type of game. Your logic for calling makes more sense if you had a pocket pair.

FLOP: I really hate your flop play. You should not be 3 betting IMO, there are just too many cards that can hit the turn that will instantly kill your hand. Any Queen,spade,Ten,King,Ace, eight are all horrible cards for you. Thats 25 cards if im counting correctly that will potentially kill your hand. Becuz your equity in this pot is going to change dramatically with the turn card you should just call the flop raise with the intention of raising a blank turn card.

TURN: You should bet, theres still a decent chance your hand is good, you cannot allow the button to take a free card if hes on a draw. If he raises and its one BB back to you, you should call. IF he raises and somone else check/3bets, you should fold.
About you saying that your fold equity is zero. This doesnt matter, if you have the best hand you should still want to get more money in the pot. Yes it would be better if everyone folded but you still make money if they call and your ahead. Although there are up to 27 cards that can kill you on the river, 2 more since if the X turn card pairs on the river you lose to any Queen(Xs is already accounted for)....With one card to go your hand is much stronger now than it was on the flop when there were two cards to come. Betting the turn is the right move IMO.