Regarding the first response, what is a, "pot?" Also, just want to make sure I'm clear, by "pulse length" you're referring to the value of pwm in the code, right?
pot == potentiometer (variable potential divider)
We don't use PWM to control servos, we use PPM, but the width of the controlling pulse is roughly 1 to 2ms, repeating every 20ms.
(yes, I know you coulld do that with PWM, but just don't, OK?
Lastly, will the servo hold the last input value indefinitely, or will it return to zero after "digitalWRite(servo, LOW);"
Well, since the last pulse was only 1/50th of a second ago, the answer must be no.
However, "indefinitely" could be a long time, and without any driving pulses and a shaft load, the servo could move.