Just need a quick confirmation from the experts here.
Using Arduino PWM output, we can supply required voltages (0V to 5V) to drive a logic level MOSFET?
Yes that will work. Many recommend adding a series 200-330 ohm series resistor between the pwm pin and the mosfet gate pin to limit current flow during transition switching of the capacitance load of the mosfet. Also if the mosfet drain circuit is wire to a DC voltage source other then the arduino +5vdc then a 10k resistor wired between gate and source terminals of the mosfet will insure that the device remains turned off in the case where the arduino might get powered off but the mosfet external voltage source is still on.
Thinking about using a 10 turn pot mapping to the Arduino output, it should be precise enough to do the job.
That should work ok, but keep in mind that the pot input allows 10bits of resolution of the analog input converter but the analogWrite command only has 256 bits of resolution, so a precision pot's capability may not be able to be fully utilized over say a quality single turn pot which may be good enough.