(a) The $\mathit{X}$-element is vanadium (V)
Its electronic configuration is [Ar] $3{\mathit{d}}^{3}4{\mathit{s}}^2$
Likely oxidation state: $+2,+3,+4,+5$
(b) $2{\mathit{K}\mathit{M}\mathit{n}\mathit{O}}_4\stackrel{\mathrm{\Delta }}{\mathit{─}\mathit{─}\mathit{─}\mathit{─}\mathit{─}▸}{\mathit{K}}_2{\mathit{M}\mathit{n}\mathit{O}}_4$ $+{\mathit{M}\mathit{n}\mathit{O}}_2+{\mathit{O}}_2\uparrow$
(c) (i) $\mathit{Z}\mathit{n}=30\left[\mathit{A}\mathit{r}\right]4{\mathit{s}}^{2}3{\mathit{d}}^{10}$
The d-orbital is fully filled in zinc (Zn). There is no unpaired electrons are available. Inter atomic bonding is weak because of which metallic bonding is also weak.
(ii) $\mathit{C}\mathit{u}=\left[\mathit{A}\mathit{r}\right]3{\mathit{d}}^{9}4{\mathit{s}}^2$
$=3{\mathit{d}}^{10}4{\mathit{s}}^1$
In aqueous medium it exist as ${\mathit{C}\mathit{u}}^{+}$loosing one ${\mathit{e}}^{-}$ but because of high hydration enthalpy it readily converted into ${\mathit{C}\mathit{u}}^{2+}$. It also show disproportion reaction because of which the reaction take place.
$2{\mathit{C}\mathit{u}}^{2+}\mathrm{}\mathit{─}\mathit{─}\mathit{─}▸{\mathit{C}\mathit{u}}^{2+}+\mathit{C}\mathit{u}$
(iii) Actinoids are radioactive in nature. They have almost similar enthalpy of actinides. Therefore, they shows more actinoids contraction than lanthinoids contraction. They have more poor shielding of $5\mathit{f}$ orbitals than $4\mathit{f}$ orbitals.