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 an extra-stability.
II) Actinides exbhit a large number of oxidation states but not lanthanides because the energy difference between orbitals of actinides are very less,so that they can exhibit different large number of oxidation states.
III) There is hardly any increase in atomic size with increasing atomic numbers in a series of transition metals because lanthanide contraction.(lanthanide contraction is the steady decrease in the size of the atoms and ions of the rare earth elements with increasing atomic number from lanthanum (atomic number 57) through lutetium (atomic number 71). For each consecutive atom the nuclear charge is more positive by one unit, accompanied by a corresponding increase in the number of electrons present in the 4f orbitals surrounding the nucleus. The 4f electrons very imperfectly shield each other from the increased positive charge of the nucleus, so that the effective nuclear charge attracting each electron steadily increases through the lanthanoid elements, resulting in successive reductions of the atomic and ionic radii).