Push-pull MOSFET gate schematic
answer 1: the Q1/Q2 provide high currents to rapidly charge and discharge the gate capacitance, even with Cmiller (drain-gate capacitance)

answer 2: using an Nchannel, without a boost capacitor, will introduce a 5 or 10 volt drop in the switch output swing.

answer 3: If you introduce a BOOST capacitor, you can use a Nchannel. Without boosting, and if you insist on good efficiency, then the Pchan or a PNP is required.