1 - Yes. If you do this daily at school, there's no reason not to do it on stage. I've seen Honor Band concerts with tuners on stage.

2 - Yes. It's not a concert. However, the longer you give in between pieces, the longer the judges have to think and write about your performance. Check what needs to be checked - if you notice something is off, kids are switching instruments, tune timpani, etc. You don't need to rehash your entire lip slur routine.

Get most of this done before you start. Before the announcement, do a quick chorale or something to get a feel for the room. Sometimes I'll send another director into the hall, do a section of the music with tricky balance, and make adjustments based on their ears. I know that for our UIL site compared to our home auditorium, tubas need to play out (probably something about stage curtains) and flutes/1st clarinets need to back off. Often the warmup room is cold, then we walk outside to the stage door, then the stage is hot, so we recheck tuning notes.