I pretty much think one of these is definitely the case, especially since the series has already established that a non-persona user can't even damage a shadow. Unless the things they're facing in PQ aren't shadows at all(possible I guess).
And yeah, Labrys has to be with the P3 crew, if for no other reason than I doubt the P4 crew would know how to do maintenance on her.
Still, she went through exactly what each member of the cast of P4 did, so I can't help but look at her as a member of that cast really.
No, for the reason I said. This was talked about in the Answer on Mitsuru's flashback.