Need help to determine whether PWM frequency is suitable
To adapt your PWM to output your required 3V for the motor, you have to calculate it as follows: 

Duty Cycle = Vr / Vp where Vr: is the voltage required, Vp: peak voltage, and Duty Cycle: is the time of the wave to be switched on / the time to be off. So 3V / 8.2V = 0.36 and this will not make an issue while working since its just a DC fan motor.

About the required flyback diode, simply any diode will do the work required as long it can withstand the current passing through it. 1N4007 is good and safe, and also cost effective.