Driving motor with Arduino

  1. Is the motor a step motor or just plain DC motor

just plain DC motor

  1. Is the disk plate used to "convert" the motor to a stepper?

No it is still a DC motor but the disk allows the computer to know where the motor is.

  1. How can I drive this motor using Arduino?

Just switch the power with the Arduino. However it depends on what you want to do with it. Do you want to use that disc to determine it's position?