Note: I'm not a choir director or PT leader (or any type of musical leader).
Our rehearsals go like this:
Worship Song ---> Opening Prayer ---> Worship
(That part flows with no breaks in between. Choir director starts off the worship song, whoever he passes the mic to begins to pray, and when they say "amen" we just continue worshiping.
Then, we start rehearsing.
Then, he gives announcements/instructions/attire, etc.
Then, he dismisses.
Our entire rehearsal lasts about an hour, never more than 90 min. and we usually get through about 5 or 6 songs (sometimes, that's 5 or 6 NEW songs). Our choir director is one of the best I've ever worked with.
IRT the second question, I think that every auxiliary should have clearly defined roles and responsibilities so everyone will always know what to expect and there are no questions about what is acceptable and what is not. And no surprises.