Is this a... decomposition reaction: Fe2O3(s) + C(s) à CO(g) + Fe(s)?

Fe₂O₃(s) + 3C(s) → 3CO(g) + 2Fe(s)
This is not a decomposition reaction. Decomposition is the reaction of a (more complicated) compound changes to two or more simpler substances. There are two reactants, and thus this is not a decomposition reaction.

Al₂(CO₃)₃(s) + 6HCl(aq) → 3H₂O(l) + 3CO₂(g) + 2AlCl₃(aq)
This is not an oxidation-reduction reaction because there is no change in oxidation number.
Oxidation number of Al in Al₂(CO₃)₃ = Oxidation number of Al in AlCl₃ = +3
Oxidation number of C in Al₂(CO₃)₃ = Oxidation number of C in CO₂ = +4
Oxidation number of O in Al₂(CO₃)₃ = Oxidation number of O in H₂O and CO₂ = -2
Oxidation number of H in HCl = Oxidation number of H in H₂O = +1
Oxidation number of Cl in HCl = Oxidation number of Cl in AlCl₃ = -1