You can enter as many PKMN as you want, but the battles are all single battles. Trainers only command their PKMN like combat sport coaches instead of play-by-play commands, except that there are no breaks, so you only get to give strategic advice before the battle, and then cheer from the sidelines.
So instead of "Pikachu, use Thunderbolt, now! Now evade with Agility, and then counterattack with a Quick Attack!", and since there is no concept of Moves, you get something more like "Try to outflank it and don't let it hit you. It's weak to ELECTR, so shock it until it goes down. It can also use some GROUND moves, so be ready to jump if you feel the floor starting to vibrate."
But of course, the more juvenile/less intelligent your PKMN, the more simplified you have to give your advice or they'll just do their own thing and forget whatever you said.
In tournaments, typically you have to pay a registration fee, which differs between the tournaments. For non-official tourneys i'll simplify the format to an Elimination-style tournament with 8 participants. So 3 battles. Winner gets a prize depending on the tournament.
For official tourneys I'll be doing Round Robin with 8 participants, so 7 battles. Winner gets to rank up in addition to the prize.
Now, if you get famous enough you can earn sponsors on your PKMN, but the sponsors will typically stipulate some demands in the contract. You have Bro, though, so he'll negotiate some good terms for you.
Re: your competitors. Different species have different base stats, so there's no hard and fast rule what average stats are going to be like. I'll usually modulate the enemies' levels depending on what challenge-level I feel is appropriate narratively. But in the rookie's cup you can assume that all your opponents are gonna be babies. So if it's a Raichu-line, Pichu. If it's a Charizard-line, Charmander. etc etc.
