Do all the players share the same universe or can I have my own universe? Can I make a particular faction win without having to fight all the other players?
The galaxy simulation affects all players, regardless of game mode they play. If you don't want to interact with anybody, you can play in solo mode, and if you want to interact with just a group of friends you can play in a private group.
You cannot join a power and then have no competition... the other player's efforts will still affect yours.