P-Mos switch high side
The questions:
  
  
  
  When Q2 is off, what is Vgs at Qsp1?
  Is it going to be Vcc or Vcc-10v?
  Will the Mosfet turn on and off with this schematic?
  


Qsp1 will not turn off reliably because it relies on leakage currents in the zener diode to try and reduce gate-source voltage to zero - use a 47 kohm resistor in parallel with the zener diode.

Qsp1 will turn on properly even if you added the needed 47 kohm I mention providing that Vcc is sufficient.

You need base resistors for both BJTs - you can't apply 3 volts to an unprotected base-emitter region. Given that you are using a p channel MOSFET for the upper switch, why not use an N channel MOSFET for the ground switch?