The forward reaction is bimolecular. any change in [A] or will modify rate. a catalyst would also change the rate of reaction. T usually increases rxn rate.
Remember that LeChat's principles of reaction equilibria deal with reversible reactions. In this case, any change in [C] will have no effect on the overall rxn rate because the reverse reaction, which is dependent on [C], does not occur. Irreversible is the key word.