Here we go:

ESC: Electronic Speed Control (Contols power to motor)

BEC: Battery Eliminator Circuit (Supplies power to the reciever)

Q:"What is a "brake" on a speed controller?"
A: A brake on the ESC stops the prop from spinning when the motor is off. This does two things: it allows folding props to fold, and reduces the likelyhood of breaking a fixed prop.

Q:"Do all Electric Aircraft Motors operate on the same voltage?"
A: No the voltage is dependant on how-many/what size the batteries are in you battery pack.

Q:"How does one size the BEC amps requirement?"
A: The current required of the BEC is dependant upon what size/how many servos you are running.

Cheers,
Grant