Without running ranges, I'd assume we're around 46% against their range here, maybe more if they are holding an overpair JJ-KK.

Once raise I think we have almost no FE is it's probably a math question of whether our range is ahead of theirs. In game I'd be playing this hand the same way you did, think flop bet is fine also.

I wouldn't 3bet this hand pre too often BvB vs an unknown.

As played, I like a check back on the flop at least some of the time, following the advice in Doug Polk's guide to playing flush draws. As played, I hate life when he makes such a massive raise. I'm going to go with the hand as the NFD + gutshot is just too strong to do anything else with other than jam but we have painted ourselves into a corner we don't always need to be in with the 3bet and then the cbet, both of which, aren't mandatory.