Evan, Dogmeat, to answer your questions...
There are four booths, but they only serve to give everyone four opportunities to vote. The person with the most votes combined is considered seat #1, second most is seat #2, etc.
The seat rankings are not meant to define your positions: I ask different questions of each of you to see how you fare in particular areas, but I could just as well ask the same questions of all of you. I was trying to motivate people to think and ask questions so they can make educated decisions. It's nice to have a variety of reps that use different methods to see which are best. The seat ranks are not meant to identify which representative has more power over another, but there are situations in which rank does matter: When ever we add, or specifically, remove a seat, at the end of the quarter it will no longer exist, and that may have effects on the final seat rank #.
Unless you want to start some project or activity, there's really no obligation to it. Your responsibilities and rights are:
You may enforce the rules via vigilance: Remind a member to behave and/or read the Rules/FAQ. If that member persists to misbehave and/or ignore the authority, it is grounds for a vote to add a strike to their record, granted a staff member is aware of the situation. This is akin to an etiquette issue.
Furthermore, you will have your own forum section to post on issues. So if member X is misbehaving on an etiquette issue, you can deal with that via a vote. If its a rule violation, just let a mod know.
You'll have some power to overturn mod judgements too, but I don't have that clarified yet, so just be patient

You're also welcome to create activities, but you are certainly not required to. To avoid rep arguements on challenges, I think a voting system will keep everything running smoothly. How the reps vote or decide on what challenge, I would rather leave that up to you. I may give you powers to pin your own topics for challenges perhaps.
Here are some guidelines that might work out:
Activities require a minimum of 48 hours to be voted upon.
Activities must receive a 3/4 majority in a vote to be approved.
etc...
Give me some time and I will hammer out a guide you can use to keep things running smoothly.