Two quick questions:
1. I've gotten a second starter set, and for a moment I was thinking of putting the damage cards from both together to make a larger damage deck, but would doing that throw off the balance or the game and not be legal in official games? The ratio of cards in the deck remains the same, but it doubles the chance of getting each card.
2. In a miniatures game with only two factions at the moment, would you have to bring two squadrons, one of each faction, to a tournament? The way the game is set up right now, faction vs the same faction hasn't been addressed, and I can see a situation where 75% of the players would show up at a tournament with the same faction.
1) Keep them in two separate piles and have each player draw from their own damage deck. Since this is how it flies according to the tournament rules, you're not exactly doing anything outside the scope of what was intended for the game. Shuffling them together would be a bad idea.
2)As people stated above, one faction; mirror matches are allowed in the tournament rules.
With that in mind, remember, those are guidelines for organized play. If you and your group will most certainly never be playing at a tournament, and want to go your own way, please do, as you'll only get more enjoyment out of it by playing it in a way you're all having fun with. Run mixed squads of Imperials and Rebels if you want to, it's your game now, so do what you want.
Have a "what if" match with Luke and Vader taking on the Emperor's finest TIE vanguard, as father and son race to destroy "The Emperor's Shuttle" (represented by the Senate Shuttle token, obviously) so they can rule the galaxy together.
Be as creative as you want to. Don't let anyone tell you that you're doing it wrong, because if you're all having fun, then you're totally doing it right. The rules only matter if you're going to an organized game, or playing with someone who isn't aware of your group's house rules, so do respect that side of it though.