The piston screws in. Pressing won't move it until you bend the parking brake screw, ruining it.
Bleeder screws do not seal when loose, so you will always have air visible if applying suction to the bleeder.
The best / surest way to bleed is 2 people, one to pump brakes, the other open the bleeder, and close after each hold down of the pedal. Some systems the sudden flow helps drag the air out.