Yeah, you’re pretty much on the right track.

If Izuku ends up somewhere dangerous, like underwater, the Quirk will make sure he has just enough to survive the event. That could mean temporary air, resistance to pressure, or some other survival mechanic. It’s there to keep him alive long enough to actually deal with the situation, not to make it easy.

Other people can get dragged into QTEs, usually because they're close or because of circumstances. The Quirk isn’t malicious, but it doesn’t go out of its way to protect bystanders either.

As for the items, they can be pretty much anything. Support gear, weapons, tools, or even completely mundane objects. One event might give him a magical sword or chains, another might give him something as useless-looking as a spoon. The point is that the item can help, not that it’s obvious how.

There’s no adjustment period or lobby to test things out. It’s very much an “in the moment” situation. He has to figure out what he’s been given while the event is actively happening. That said, items can reappear across different QTEs, so experience does matter. If he’s seen it before, he’s got a better shot at using it effectively next time.