Do I have to register with a team to get my curecoins or can I leave it team 0?
For CureCoin, you MUST be folding for team 224497 (CureCoin Team) in order to earn CURE
Why not open curecoin up to all teams?
I'm not sure I know the full answer. I'd recommend asking on their ANN:
https://bitcointalk.org/index.php?topic=603757.3080My guess would be:
1. CureCoin probably felt teams don't want members who are folding with an unfair advantage competing against those who don't (monetization vs philanthropy). That was mentioned on the ANN somewhere.
2. FoldingCoin does let you stay on your own team, BUT you have to change your username (that's why if you want to merge-fold, you have to change your username to the FoldingCoin format)