Haven't tried it but worth a shot.
Not really.
Even a small "refrigerator magnet" can have a magnetic field thousands of times greater than what that sensor is designed to measure. You will simply overload it.
To measure shaft rotation, some people use magnetic sensors designed for the purpose. Allegro Microsystems make several varieties.
Or consider the simple and cheap motor shaft encoders by Pololu, which divide the circle into 20 segments. Those would need some zero position indicator, though.