(D) $(i)$ $A$ momentary deflection occurs in the galvanometer due to the change in magnetic flux linked with the coil.
$(ii)$ $A$ momentary deflection occurs in the opposite direction because the change in magnetic flux is reversed.
$(iii)$ No deflection occurs because there is no change in magnetic flux when the magnet is stationary.
$(b)$ The phenomenon is called Electromagnetic Induction. It was discovered by Michael Faraday. The law that relates the direction of induced current to the direction of motion of the magnet is Fleming's Right-Hand Rule. It states that if you stretch the thumb,forefinger,and middle finger of your right hand such that they are mutually perpendicular,then the thumb points in the direction of motion of the conductor (or magnet),the forefinger points in the direction of the magnetic field,and the middle finger points in the direction of the induced current.