I would expect that the noise you are experiencing is PWM hum, the only way to solve this is to make your PWM switch at much higher frequency which i i have NFI how to do on an Arduino. As far as the continuous pots, PID seems to be the way to go here, it will require some complex maths but it should work. A short intro here if u don't quite get it. Basically your motor driver would be told "move motor forward a bit" and would send PWM signal to motor to turn forwards. The controller then looks at the value that the pot changed and compares it to the change in PWM signal it sent. it does some maths here and thinks, if i want to turn it x amount, i change the PWM signal by x*4 (for example) and it does this constantly, adapting for changes in torque etc. this enables much higher amounts of accuracy. As to how to code this, it'd be fun, but quite challenging.