1. Do I have to be either a beginner trainer, a gym leader, or an Elite 4 member, or can I be an adult that starts out with a couple of older pokemon?
You can create whatever you want to be. If you wish to be a trainer or something else not part of the Elite 4/Gym Leaders, create it in Character Creation.
2. Am I allowed to start with a couple of beginner items? I started mine off with a couple of balls and some food, but I'm not sure that was allowed. (Feel free to take some money off for that if it wasn't allowed or PM me to take some things off the list.)
We haven't actually got a rule for that but one is being made. (Or will have been made by the time you read this)
3. Can you only start with one single level 5 pokemon? This ties in with question one, because if you sign up as a Team Whatever (something I wanted to do, whenever there is more information on them), would I be able to have 2-3 lower to mid level pokemon? Like a level 10 or 15 maybe?
One single level 5. No team rules yet.
4. Are characters without pokemon allowed? Not that anybody would want to be one, but it's not clear whether you can or not.
Yes, this is allowed.
5. What are the rules on psychic characters? Are there any? My character is a psychic and I was wondering how far I can go with that. From what I know of, they seem to be able to see snippets of the future and levitate small objects. I don't think they can read minds, but I can't remember if they do or not.
Psychics in Pokemon can't read minds or anything like that as far as I can see. However, they can levitate a few things and use those as attacks. It may however not be advisable to attack another trainer with these skills!!
6. The hunt for Victini; what is that about? Is there only one Victini? Or can anybody participate? Or do they have to be in the region?
One Victini.
Anyone can participate.
7. What does it mean when gym leaders can't travel? They can't go anywhere, ever? Sometimes gym leaders go places. In fact, every effing gym leader in B/W never seems to be home!
I will refine the rule for clarification.