I sincerely hope that I'm not going to annoy everyone with my noobie questions.
Of course not! "noobie" questions are the most fun to solve, because they're not as complicated as the questions us experienced people ask! ;D
How many shields can be used with the Arduino?
There's no limit, as long as together they don't draw more than ~500mA from the +5V pin, and they don't interfere with each other by using the same pins.
Would the Arduino have enough inputs for all of the above?
Impossible to say, without knowing how many pins the FM receiver shield takes up. I would say it should be possible, but you may end up using Shift Registers and/or Serial-enabled LCDs.
Also, can the Arduino run two separate displays?
Assuming you have enough pins, yes.