Those 10 cards are the cards you use during the tournament, so of course you can't use them anywhere else. If you lose them you'd have less cards to play the tournament with :S
I played lots yesterday until it decided I wasn't in a game and stole 5 of my best cards. Cheating system :<
Probably a subtle hint for me to quit.
Had a bug where I won two TT tournaments in a row but no new achievement.
Yeah, you should think about adding card rewards though, that would be cool.
I may actually make the avatar cards rewards for winning tournaments, that'd be pretty cool I think!