I) Cr²⁺ is strongly reducing in nature. It has a d⁴ configuration. While acting as a reducing agent, it gets oxidized to Cr³⁺ (electronic configuration, d³). This d³ configuration can be written as t₂³g configuration, which is a more stable configuration. In the case of Mn³⁺ (d⁴), it acts as an oxidizing agent and gets reduced to Mn²⁺ (d⁵). This has an exactly half-filled d-orbital and has extra stability.
II) The actinoids exhibit a larger number of oxidation states than the corresponding members in the lanthanoid series because they are bigger; the outermost shell is further away from the nucleus, which means the ionization energy is lower for the corresponding oxidation state compared to lanthanides.
III) Due to partial absorption of visible light, the electron from one orbital gets promoted to another orbital of the d-subshell. Due to the presence of unpaired electrons, transition metals are coloured.