Why do zero gravity flights not stall?
The aero-dynamics of a flight in reduced gravity are different than a flight operating in normal conditions. When an aircraft is experiencing zero gravity, it does not stall because the wings are not generating any lift, because the aircraft is in a state of weightlessness.

In the paper for the requirements for zero gravity flights, it is mentioned (PDF):


  ... zero G flights stalling conditions are different as compared to
  conventional flight maneuvers, because the plane is weightless and is,
  therefore, in no need of aerodynamical support. On the other hand, a
  minimum speed is required to execute the delicate control through the
  parabola. For this reason the stalling speed is taken as the minimum
  aircraft velocity required for effective control.