Should an entire compound or just the redox-active element be written in redox pairs?
You generally use whichever compound is actually present in solution.

For manganese(IV), it will practically always be $\ce{MnO2}$ so use that. Manganese(VII) will always be $\ce{MnO4-}$ so use that. Manganese(II) salts dissolved in water dissociate and coordination complexes of manganese(II) are very labile. Thus, it doesn’t make sense to assume any $\ce{[MnL_n]^2+}$ complex to predominate and you should simply use $\ce{Mn^2+}$.

It does, for example, make a difference if your iron redox pair is $\ce{Fe^2+/Fe^3+}$ or $\ce{[Fe(CN)6]^3-/[Fe(CN)6]^4-}$. Likewise, a reduction using tin(II) should better be written $\ce{Sn^2+/[SnCl6]^2-}$.

If you are in doubt whether something dissociates or whether it should be considered a single entity, the cleaner solution is probably to write the fully dissociated salt, so you can get away with using $\ce{Sn^2+/Sn^4+}$. However, as soon as molecules or oxyanions are involved you cannot resort to this; oxalate reductions have to be $\ce{C2O4^2-/CO2}$ and permanganate has to be $\ce{MnO4-/product}$.