Is a combustion necessarily a redox-reaction or can there be exceptions?
Yes, every combustion reaction is a redox reaction. Combustion is an exothermic reaction of a fuel and an oxidant (that's a big clue). Most commonly, the oxidant is oxygen, which is reduced to water in the process. The other products will depend on the fuel. Organic compounds will have carbon atoms of various oxidation states that will be oxidized to the +4 state as carbon dioxide product.