(a) The Mn$^{2+}$ ion is an oxidizing agent because it can be easily oxidized to Mn$^{3+}$, which is a stronger oxidizing agent. On the other hand, Cr$^{2+}$ is a reducing agent because it can easily be oxidized to Cr$^{3+}$, which is more stable.
(b) The greater atomic contraction across periods in the periodic table is due to the increasing nuclear charge, which pulls electrons closer to the nucleus. However, lanthanides exhibit only a small contraction due to the f-orbitals shielding.
(c) Transition metals have the ability to form interstitial compounds due to their small atomic size and the presence of vacant spaces between the metal atoms, allowing small atoms like H, B, C, and N to occupy these spaces.