Electro magnetic induction is the phenomenon involved here.
(i) The galvanometer will be deflected.
The coil which is connected to battery will act as an electro magnet ( coil B)
So whenever there is a change in magnetic field ( coil B) , an emf will be induced in the coil A and the galvanometer will be deflected for a moment.
As soon as the current becomes steady through the coil B, the galvanometer comes back to the previous position
(ii)The galvanometer will be deflected.
Because initially there was a steady current flow, but whenever the key plugged out, the current decreases to zero. This change in current causes a change in magnetic field in coil B.
Thus there will be an emf induced in the coil A and galvanometer will get deflected
(iii)No change will be there
Because both of the coils are moving with same velocity and in the same direction, ther will be no relative speed for any of the coils.
So there will not be a change in magnetic field and thus no emf will be induced
So no change will be observed.