(A) Iron is a better conductor. The reason is that electrical conductivity is inversely proportional to resistivity. Since the resistivity of iron $(10 \times 10^{-8} \; \Omega m)$ is significantly lower than that of mercury $(94 \times 10^{-8} \; \Omega m)$,iron allows electric current to flow more easily.
$(b)$ Material $A$ will behave as an insulator. Insulators are materials that offer very high resistance to the flow of electric current,which corresponds to a very high resistivity. Since the resistivity of material $A$ $(10^{10}-10^{14} \; \Omega m)$ is extremely high compared to material $B$,it acts as an insulator.