1. When the transistor is ON, the two resistors should give about 18 V at the MOSFET gate. However, this requires a drive voltage to the bipolar of at least 20 V, since the emitter would be at 18 V. Probably better to ground the emitter and put R2 from the collector to ground.
2. Yes, when the transistor is OFF, there would be 36 V from collector to emitter. If you ground the emitter and put R2 from collector to ground, then the maximum voltage would be only 18 V.
3. With these two suggestions, it might work. It depends on the switching frequency and the device capacitances.