What is the use of potassium permanganate $(KMnO_4)$?

Which of the following statements is incorrect for $KMnO_4$?

Potassium manganate $(K_2MnO_4)$ is not formed in which of the following reactions?

The spin only magnetic moment $(\mu)$ value $(B.M.)$ of the compound with strongest oxidising power among $Mn_2O_3$,$TiO$,and $VO$ is $....$ $B.M.$ (Nearest integer).

The amphoteric oxide of Vanadium $(V)$ is $V_2O_5$. It reacts with alkali to form an oxoion '$X$' and with acid to form an oxoion '$Y$'. The oxidation states of '$V$' in '$X$' and '$Y$' are respectively:

Correct statement for $CeO_2$ is/are:
$1$. It is diamagnetic in nature.
$2$. It is a good oxidising agent.
$3$. It is a colourless compound.