Permanganate $\Rightarrow MnO _{4}^{-}$

$2 \times 2 P _{\pi}-3 d _{\pi}$

$1 \times 2 P _{\pi}-4 P _{\pi}$

$(2)$ $MnO _{4}^{2-} \Rightarrow$ green

$MnO _{\stackrel -4} \Rightarrow$ purple/violet

$(3)$ Manganate contains $1$ unpaired electron hence it is paramagnetic

where as permanganetic contains no unpaired electrons hence it is diamagnetic.

$(4)$ Both have d's hybridisation hence both have tetrahedral geometry.