3 bet bluffing range pre multiple questions

Thoughts on having this in our 3 bet bluff range pre?

Not in mine
However if you know the player in MP really well, or if you're both deep stacked, or ...

Whats the logic for it not being in yours, just too weak ?

For me J8s is too wide. I would 3bet bluff here stuff like A2s-A5s and 56s-89s. Maybe sometimes one gappers like 79s but only occasionally against players with high F3bet. And to your questions:

1) It is one of the better flops for you so you should probably cbet here almost always. Put pressure on hands like AK, AQ.
2) He might call you once with A high air so you should probably fire again OTT when you pick up extra equity. You dont have any showdown value so the only way you can win the hand is by making him fold. And one of the reasons you 3bet bluff with suited hands is that you can pick up a lot of semi bluff which can be barreled. So this is a good opportunity.
3) If you dont pick up any extra equity you should consider 2nd barrel according to the turn card and the opponent. Tight opponents are likely to fold flop already if they have nothing so on a blank it is unlikely you will make them fold turn. But against someone more loose you can definitely try firing again on many cards. You still have a gutshot.

J8s as a 3bet bluff BTN vs MP would be looser/more aggressive than usual. I wouldn't mind doing this vs weaker opposition or vs guys who fold more than 60% of the time vs 3bets.

your hand falls under the Bet Flop category most of the time, with a gutter + backdoors

on the turn with position, you can definitely consider mixing checks here. Vs someone who raises more often, check this more often. As a general rule of thumb, I would check the top 50% of draws and bet the bottom 50% of draws (that are not strong enough to bet/call). Of course if you had Jc9c, just bet and commit yourself (if he jams you have 25% equity so you only need 25% pot odds to call off)

you can't really go wrong with betting here, that's also usually my default option here but if you go deeper into analyzing your various options, and the possible counterplays from your opponent, then certainly i think this is a good candidate to check. I would bet/fold J9, check J8, bet/fold 98, check AcXc, bet/fold small flush draws, bet/call A2cc/A2dd/A3cc/A3dd/A8cc/A8dd etc