No, you can't register a team. There is some strange addon that a few people use to make themselves feel cool, but don't waste your time on it!
You can sign up with a party into any of the battles.
And yes, play arenas - they're a much better way to improve. It's possible that you may find yourself losing a lot near the beginning, but just think of it as a challenge; a test. Work yourself, and quickly you'll see your skills become honed and strengthened.
The team aspect of it is great. Try to get vent with your teammates so you can really practice your communication and planning.
Have fun