Statement (I): This statement is incorrect. Dimethyl glyoxime forms a square planar complex with nickel, not a six-membered covalent chelate, when treated with NiCl$_2$ solution in the presence of NH$_4$OH. The resulting complex, known as a nickel-dimethylglyoxime complex, is characterized by a square planar structure where the nickel is coordinated by the nitrogen and oxygen atoms of two glyoxime molecules.
Statement (II): This statement is true. Prussian blue (Fe$_4$[Fe(CN)$_6$]$_3$) is a coordination compound containing iron in both +2 and +3 oxidation states. The compound forms due to the combination of Fe$^{3+}$ ions and [Fe(CN)$_6$]$^{4-}$ complex ions, leading to a structure with mixed oxidation states of iron.
Conclusion: Statement I is false, and Statement II is true.
Match List - I with List - II:
List - I:
(A) \([ \text{MnBr}_4]^{2-}\)
(B) \([ \text{FeF}_6]^{3-}\)
(C) \([ \text{Co(C}_2\text{O}_4)_3]^{3-}\)
(D) \([ \text{Ni(CO)}_4]\)
List - II:
(I) d²sp³ diamagnetic
(II) sp²d² paramagnetic
(III) sp³ diamagnetic
(IV) sp³ paramagnetic