Being a Lions fan is a gift...
...and a curse.
1) Catapults: Can they attack outside the shield?
My understanding is that nothing can shoot through the shield (from either direction) until it has been deactivated.
2) Cards that can't be used. Is there any solution to this? Near the end game, all that was left of the Naboo was the Purple queen, Qui-Gon and Obi-wan. I used that card to make all my hand cards Theed cards, so 3/4 of my hand I couldn't use. I was forced to use unplayable cards.
At this point I think you have no recourse. You just have to play cards that will do something and hope you'll draw more usable cards on future turns.
3) Droid control ship battle: When Anakin fails, the two dice are removed and rolled again when he tries again later?
Yes. Every time Anakin tries to move through a card/space the blocking dice and Anakin's dice are re-rolled.
And lastly some advice to first time players, don't forget the pillars in the palace. =) We totally forgot... we were walking right through them.
It's pretty easy to forget this. Thankfully it's not a big game-breaker.
Great first game.
Glad you enjoyed it.