You have a party of 6 pokemon. And that is your team.
As for the question about trading.
When I was a kid, everyone traded pokemon with each other, and it was a huuuuuge part of the game experience since it was so social. People aslo battled against each other a lot. I always battled my brother after we had beaten a gym in our repective games, like a real life rival xD
So yes, trading (and battling) with people increases the fun of the games exponentially. However, in the state that the series is currently in, it would be hard to trade and battle with people nowadays.
You should try playing pokemon. The games have a kiddy stigma on them, but the gameplay goes beyond age. The first playthrough is always the most memorable. Catching your first wild pokemon, watching them evolve for the first time, beating that pesky first gym leader, it's great fun.
I LOVE ICELAND!
