Barry Doesn't Save Jill?
If I remember correctly it was Barry that saves you from the booby-trapped shotgun room if you're playing as Jill. Is there a certain part in the game you have to complete before this happens? Or do you have to go looking for the broken shotgun like Chris did in the 2002 remake?
And Barry and Jill finding Forest altogether?
Same. It's my 2nd playthrough as Jill (loaded save and started "Once again...") and he saved me on first.
I never triggered any other cutscenes with him.
There is no limit to the amount of times he can save her, however I always go for the broken shotgun as it's more straightforward and guarantees you'll get out with your life (just in case Barry saving Jill doesn't trigger).
The room with the broken shotgun is in the West Corridor, it's the only other room in the corridor with the safe room (Medical Safe Room). Jill fortunately has the lock pick to open it (whereas Chris needs a small key).
Sorry for necroing this, but I've now run into this and searched for what happened, and I think there could be some confusion, as what happened to me. Because that meeting you're talking about (the one in the main hall after you get the Sword Key), Barry NEVER gave me anything, and just went on his way, and then he never came to save me in the trap room. Him never giving Jill anything in there could have happened to some people, too.
I think this could be because of your inventory being full at that point. I checked a recording of my playthrough, and I was indeed carrying too many things for the game to have him think of giving me anything at all. This could be the problem people are running into here. They never get the ammo you're talking about (hell, Barry never mentions he has anything to give to her), they get into the trap room, she dies, they expected something else, come here, see that there's a cutscene you can't let happen if you want him to save you, but to them, that's not the cutscene THEY saw, which makes them think this was not the same scene. But it could very well be.
I think the better tell if that's the scene he's SUPPOSED to give them to you. For reference, this is the scene where he tells you there must be a back door somewhere to plan an escape route. I'm guessing this is where he's supposed to give the rounds to you, but if you don't have the space, the game never clues you in on anything. In other words, this could be an oversight on the devs to not think this possibility through that people would get confused that their game could just be bugged, and no one ever thought to tell players to make sure they had a slot in their inventory so he could give those to you.
EDIT: Just to confirm, I went through the game to make sure that this was the case, and yes, the reason he never gives you the acid rounds in the Main Hall encounter is because you don't have any space in your inventory. If you do, there'll be added dialogue in the scene where he gives them to you. If not, the game completely skips that part. Regardless, you have to try to get the shotgun before that encounter no matter if he is able to give you the rounds or not in order to get the Jill Sandwich scene, AND make sure you have a spot open in your inventory before triggering that scene (I think it triggers if you enter the Main Hall after grabbing the lighter), since those rounds will come in handy.
No idea why Capcom thought it was a good idea to confuse players into thinking it was a bug when it was a feature, but hopefully this clears up the confusion.