Sorry . . . but you asked.
The number of possible parties depends on where she is going through recruitment. In regard to Pref, generally it's 2 or 3 parties (this also depends on her university).
Regarding your double-blind question, the PNMs know who invited them to parties, and the GLOs know who accepted their party invitations. Unless something is said at the parties (which I think is not allowed), neither should know the other's choices (there are vague ways of communicating how much a PNM likes a GLO and vice versa without breaking the rules). The actual bid matching process is kind of confusing to explain, so I won't try. However, the GLOs get the list of their NMs before the NMs find out where they got a bid.
I can't imagine not being able to know
any info--look how impatient we get for info in retro recruitment threads!!! Hang in there, momof3--we're rooting for your daughter to find her home away from home.