I am clueless with this one...please help, i know that it might be hard to explain but can someone at least try?
a. Ok initially there is a magnetic field flowing through x which goes from right to left or the futhermost right coil of X has a south pole. So when you remove this, a north pole will be induced on the left side of Y (this occurs because when the south pole is removed, the coil y will oppose this change and create a north pole). Now a north pole will mean there is an anticlockwise current flowing, hence it will flow from left to right through the galvanometer ( the direction of the current is right).
b. When the resistance is increased, this will have an effect of "weakening the south pole" or maybe better put will cause a decrease in flux present at the right side of X, this will be counterbalanced by producing a north pole in coil Y and consequently the current will flow in the same direction as scenario a, that is right.
c. Reducing the resistance will have the opposite affect, and increase the current this will "increase the south pole present at the right side of X" and therefore counterbalanced/ opposed by producing a south pole in coil Y which will produce a clockwise current, going left through the galvanometer.
It is hard to give an explanation without any images and i hope you can understand these explanations and that they are correct.