Catching up a bit again with you guys. Yes, four moves is the max, staying in theme with the pokemon games. How specific moves work (because taking statistics out of a game doesn't always translate smoothly to a freeform RP) you can ask me in a PM or in this thread.
The level of a specific pokemon doesn't have to be specified, and I suggest to leave it out completely. You can still use an approximate level to check which moves you can have on seribii.net and bulpapedia, though if you give yourself a definite level, you'd have to level up occasionally to learn new moves, and keeping to such statistics can severely hamper RP. Learn a new move when its appropriate in the RP and let you approximate level keep in touch with that of the team, unless the trainer specifically trains you harder than the others. I believe this is the best approach for now.