Do I own a token that I create under somebody else's control?
No, that token is owned by the other player.  From the current Comprehensive Rules:


  110.5a A token is both owned and controlled by the player under whose control it entered the battlefield.


Tokens used to be owned by the controller of the effect that created them, but this was changed in the Magic 2010 rules revision to line up better with people's intuitions about ownership of permanents.