(N/A) $(i)$ Osmosis is the process responsible for the gathering of water in the hollowed portion of $B$ and $C$. Since the concentration of solute (sugar in cup $B$ and salt in cup $C$) is higher inside the cup as compared to the water outside,water moves from its higher concentration (outside the cup) towards the lower concentration (inside the cup) through the semipermeable membrane of the potato cells. This process of inward movement of solvent is called endosmosis.
$(ii)$ Potato $A$ acts as a control for the experiment. It is necessary to provide a baseline for comparing the results and to demonstrate that the movement of water is due to the concentration gradient of the solute.
$(iii)$ Water does not gather in the hollowed portions of $A$ and $D$ because:
In potato $A$,the hollowed portion is empty. Since there is no concentration difference (no solute),no osmosis occurs.
In potato $D$,although it contains sugar,it is boiled. Boiling kills the potato cells and destroys the semipermeable membrane,which is essential for osmosis to occur. Therefore,no water movement takes place.