With K7x I'd just have bet the flop with the intention on barreling half the deck on the turn and river.

We don't rep much on the turn is the only problem if we beat, are they a reg or a rec?

good barrel spot i think and likely a good tripple barrel spot depending on river most of his range is weak middle pair+draw type hands and we don't mind folding out his AJ either. Never played zoom or speed poker though so i don't know how the games play.

You have some equity and not a lot showdown value so I'd be inclined to bet here. Checking isn't terrible by any means, but I think bet will be slightly better given the average player type.

As played villain is usually capped if he's not betting the turn, you still have some equity and again not a lot showdown value so I'd be inclined to bet here also.

I'd be betting flop. You say it's not a good board to rep but I really disagree. As the button raiser here you have all straight combos, all sets, all 2 pairs, all overpairs and strong pairs as well. There are a TON of strong hands you can rep on this board.

When villain checks to you again on the turn I'd fire as well. His range should be pretty weak when he doesn't lead the turn so I'd expect to have a decent amount of fold equity combined with the actual equity of your draw that makes it a pretty good spot.