(A) $(i)$ The atomic number of $Q$ is $13$. Its electronic configuration is $2, 8, 3$. Since it has $3$ valence electrons,it loses $3$ electrons to achieve a stable octet. Thus,the valency of $Q$ is $3$.
$(ii)$ Elements with atomic numbers $12$ ($P$: Magnesium) and $13$ ($Q$: Aluminium) are metals. Element $14$ ($R$: Silicon) is a metalloid. Element $15$ ($S$: Phosphorus) is a non-metal.
$(iii)$ $P$ (Magnesium) will form the most basic oxide. In a period,metallic character decreases from left to right as the nuclear charge increases,making it harder to lose electrons. Since $P$ is the leftmost element among these,it is the most metallic and forms the most basic oxide.