Is it normal that the characters that may be controlled in-game don't fight, when a player isn't switched to them? (For example Anakin, when you're playing as Kenobi in the prologue.)
That is normal, in all of the various LEGO games. The computer controlled characters will only do something when it is absolutely required in order to move the game forward (such as switches that have to be pulled at the same time).
They will not fight. If you play single player it is completely up to you to win the battles.
Yes, it's normal! There are some characters that can't fight (exemple: C3PO, Anakin, etc.)
Here's a list of all characters and their abilities. This list came from Lego Star Wars: The Complete Saga, but the majority of the characters are the same.
Look the "Weapon" column and all the characters that have "none" can't fight!