Aganju:
1. Yes you can join as many fellowships as you would like.
2.you can only join a team for a game type in one fellowship but can join teams in any fellowship, eg, you can be on the checker team in fellowship A. but not B. at the same time, you can however be on the checker team in fellowship A and the backgammon team in fellowship B, therefore there is no conflict.
3.every team has a captain and determines who plays on their team, some by ratings some by first come first serve.
4. some like to be "the best". Also the bigger the fellowship, the more active it is, usually
5.most fellowships have descriptions on their main page, you can click on these names to read them http://brainking.com/en/Fellowships

Good Luck