My history of Beatles Trivia Apps was one i downloaded from iTunes that had about 50 questions that anyone who had a basic grasp of the band could get right, it also didn't look good and got dull pretty quickly. I personally would like a trivia app to be harder as it goes along, instead of having different grades of difficulty that you can just jump into from the start.
I'd say be sensible not paranoid when you build it. Apple wont sue if there is no music or footage that belongs to them and its made clear its not officially endorsed, licensed, ...