Step 1: Reduction with alkali metals. Co\(_2\)(CO)\(_8\) is reduced by Na to give the cobaltate carbonyl anion:
\[
\mathrm{Co_2(CO)_8 + 2\,Na \rightarrow 2\,Na[Co(CO)_4],}
\]
so (A) is true.
Step 2: Carbonyl structure. One isomer of Co\(_2\)(CO)\(_8\) has two bridging CO ligands (not three); the other isomer has all terminal CO ligands. Therefore (B) is false.
Step 3: Preparation. Co\(_2\)(CO)\(_8\) is prepared by reductive carbonylation of cobalt(II) salts (e.g., cobalt acetate) under CO pressure \(\Rightarrow\) (C) true.
Step 4: Isomerism in solution. In nonpolar solvents like hexane, Co\(_2\)(CO)\(_8\) exists as an equilibrium mixture of the bridged and unbridged isomers \(\Rightarrow\) (D) true.