Answer
See the answer below.
Work Step by Step
a) Number of moles of nickel (II) acetate:
$0.500\ g\div 176.78\ g/mol=2.83\times10^{-3}\ mol$
From stoichiometry, same number of moles of nickel (II) formate.
$2.83\times10^{-3}\ mol\times 148.72\ g/mol=0.42\ g$
b) Nickel (II) is paramagnetic since it has two unpaired electrons ($[Ar]\ 3d^8$).
c) Number of moles of nickel (II) formate:
$0.253\ g\div 148.72\ g/mol=1.70\times10^{-3}\ mol$, same as nickel metal.
$1.70\times10^{-3}\ mol\times 58.693\ g/mol=0.10\ g$
Nickel atoms are paramagnetic with two unpaired electrons ($[Ar]\ 3d^8\ 4s^2$).