When I can, I like use exploration Tip mission to find those badges. The mission flag takes you right to it. No wondering around until you find it ... left, right, up, down.
I think the OP is referring in posi the door to inside the dam and everyone disappears. Yeah, the first few times you probably need someone to show you the door. Call out to the group that you're lost and I'm sure someone will come back for you.
Your costumes will only be there if you save them from the costume editor. Each of your characters has to go to an Icon, Facemaker, trainer or during character creation.
I store my costumes in my ring.💍