You are correct, the common is the neutral.
Not knowing that control I can not say for certain what M1 and M2 are. However if there is also a Cool and Heat spade connection with the other 2 motor wires attached, then I think your assumption about M1 and M2 as being the same as Park is correct. You can move either wire from the M spade to the Fan spade. The only difference between the wires is the motor speed you'll have.