The word you're looking for is transistor. There is a whole section of the forum devoted to the subject of powering stuff via transistors and so on.
Forget the idea of powering anything from a PP3 9V battery. They're a hideously expensive way to get a feeble amount of current, and most of the energy they give you will be chucked away by the Arduino's voltage regulator. I suggest you look at a set of four AA rechargeable NiMH or similar in a holder.
I assume you have ample space inside your Nerf Firefly (whatever that is). Most of the problems you're describing are purely hardware and styling issues and nothing to do with Arduino, but the functions you're describing sound pretty straight forward to control with an Arduino.