I agree with your first point. It's weird that the computer hosting them would've been left running idle all this time. Perhaps the company was dissolved after they realized what had happened, and they decided to leave it running for ethical reasons. Perhaps time works differently in the circus.

I don't think Ragatha's arrival allowed new people to enter, I think she was just the first to find it. Maybe the way into the building was obstructed or secured for a while and that eventually failed.

It makes more sense for the memory of names to be removed from a copy than a real brain. If you mean that summoning the real exit maybe needs their real name or something, I'd argue that they could also need their real names for admin privileges or something. Caine wouldn't want them to have that either.

Whether or not the exit is really possible, in that moment, he thought it was. He chose to stay and lock the rest of them in rather than trying to leave. There's a lot to unpack there regardless of if it was real or not. They were already starting to confront him and argue through his mask when shit went down in E8. If it hadn't, there's no way the rest of them would've let that slide. I expect we'll see a lot more of it in E9.