I found a 3 pin buzzer with labels F, M, G for pins. What do those letter mean?
Feedback, Main and Ground.
Can I drive it like a 2 pin buzzer with one pin to positive rail and another to a FET driving a square wave to ground?
Yes that will work, although it's piezo and therefore capacitive, so it will be louder when driven straight off the output off a microcontroller, assuming the voltage is equal. If you need to drive it at a higher voltage, with a transistor, then you need a resistor in parallel, to discharge the capacitance.
Will the RE46C100 drive it louder than just a FET?
Cheers!
Yes, that IC will drive it louder because it has a push-pull output and drives it at the resonant frequency.