Why is copper(II) carbonate not selected as an unknown compound for back titration? (Whereas another unknown carbonate is used instead?)
Copper is a transition metal. As such, its ion will be a Lewis acid. The effect will, as with iron, be stronger with increased charge--so Fe(III) salts of strong acids give acidic solutions, more so than Fe(II) salts of the same acids. 

This is because lone pairs can be donated into the empty d or hybrid orbitals from water. The structure produced in this way tends to lose hydrogen ions. This means that the acidity in your experiment has two sources for hydrogen ions.