How does this motor drive circuit work?
The FET controls the motor.  The diode is not part of the control as such.  The diode is there to kill off any voltage spikes that occur when the FET opens and the motor is turned off.  The diode will only be forward biased when the motor shuts off (the FET opens.)  The coils in the motor can generate a pulse higher than the supply voltage.  The diode would short out any such pulse and prevent it killing other parts of the circuit.

The capacitor is there to filter out the RF garbage that the motor puts out - the sparking you can see on a DC motor causes RF interference.  The capacitor absorbs that and makes the motor much quieter (RF wise, at least.)

I would assume that Rx is planned for use when a different opto-isolator is used - an isolator in which (for what ever reason) the base of the BJT floats up and could cause spurious operation of the motor.