(1) No, you cannot connect your stepper motors directly to the PMDX-126. You must use stepper motor drivers suck as any of the GeckoDrive models and any of a number of other brands. To wire the stepper motor drivers, see the diagrams in section 2.5.2 of the PMDX-126 manual.
(2) You will need a power supply for your motors, typically 24VDC to 80VDC, but the actual voltage and current ratings depend on what motors and motor drivers you have. Refer to the manual for your stepper motor drivers. You can also look at the manual for the PMDX-137 for sample voltage calculations.
(3) If you enable the "charge pump" on the PMDX-126, then, yes, the PMDX-126 will prevent any movement until the PC boots AND your motion control software (Mach3/4, etc.) is running and enabled.