I think 3bet shove preflop is fine. He seems to be loose although the sample size is small. 3bet shove is ok readless anyway. In a hu match, and only 28bb deep, if we shove and wins down the 3bb pot, it is really good for us. And the chance he calls and have a better hand than ours isn't very high and even in that case we still have mb 30% equity of the pot. Also we are out of position, so by flatting, we will have a hard game on later streets.
As played, I won't go all in on flop. I would check/raise non all in or call. The reason for check/raise is mainly to make him think that we rep nothing and we are bluffing and calls with hands like K high, Q high or make a float/reraise as bluff. So, if we decide to check/raise, we really shouldn't fold it. As played, I don't think villain would only have flush. Actually if I was him I would shove most flush draws on flop since I would expect a lot bluffs from your part and even if you have A or 7 I still have like 30% equity share again. If we look at his play, I think he more likely to have Ax, 7x, a good heart and some bluffs.
We need 33% equity to make the call here. Against Ax we are doing very well with an 8h. Against 7x, we might still have 11 outs which gives us almost 25% equity. And we are crushing all the bluffs and good hearts. So, should be easy call imo.
Also I think the circumstance of the game shouldn't matter for our decision. We should just take the most +EV line in hu matches.