Whether power is provided or not should be mentioned in the materials you receive from a show host. If not, contact them prior to the show and ask. And don't wait 'til the day of the performance! (It may also be spelled out in your circuit's rules, possibly under the things show hosts are required to provide.)
When I used to work with an amplified pit way back when (96-98?), power was always provided by the show host, but that might vary by competition circuit. Whether the mixer needs to be run by a student or staff member may also vary by circuit. (I did the board myself.)
As for equipment... One thing I didn't see on your list is an amplifier. If you're not using powered speakers, don't forget an amp! (I found it convenient to avoid powered speakers because then you've only got one set of wires at each speaker to worry about.)