The stones were destroyed before the remaining Avengers found Thanos. That's why they went back in time. And they needed Tony not to be killed by the snap (hence Strange's bargain) so that he could invent time travel without relying on the time stone.

I imagine the stones would survive it, just fall out of the vanishing gauntlet. It's not like the stones were a part of it, they were just being held in place by it, but then there's the question of whether or not the contents of people's pockets got snapped as well, we know the pager Fury had didn't count as "part of him".

And no, they used the ant man tech to go back in time, no stones there.

But also: what if Thanos himself got snapped out, along with the power glove (because for some reason it turned their clothes into dust, too)? The heroes would have been fucked, right? It’s been a minute since I saw the movies but IIRC, they used the time stone to go back in time. But what if the stone was gone because it was part of Thanos’ attire? He himself used the stones to destroy the stones, so there is probably a timeline where he got snapped away with everyone else, destroying the stones in the process.

It might not be possible, since the stones were also performing the action, and Thanos didn't want to destroy the stones while snapping everyone in half. Otherwise, they might just self-destruct by going for the nearest target first (Thanos), and stop there, not fulfilling the desired action. You'd have to destroy/scatter them separately.

I don't think that they used the time stone to go back in time, since it was destroyed when they got there. They had to get it from the past, since a decent part of the movie surrounded that.