It's probably not code to leave it exposed without drywall, but i agree that switching to a water resistant insulation is gonna be better in the long run.

I don't know your build or what happened, but generally speaking, the vapor barrier is intended to keep moisture out of the wall, not out of the room. In fact it should keep it in the room.

That being said, concrete does sweat, so foam board instead of fiberglass directly on the wall is still likely better and potentially where your moisture came from.

This is probably the best recommendation, honestly. I've also heard of people doing foam board against the concrete and then batting over that.

I also second the other recommendation to see if there's code specific to your area since it is likely high moisture/humidity

That looks like paper face to me, which means the vapor barrier is built in. However, it should have extra flaps on the side that you staple to the studs to close up the vapor barrier (otherwise the studs become a point of ingress for moisture into the insulation)

I'm confused on who you were trying to reply to.