1. The law of conservation of mass applies to this reaction because when you look at its balanced chemical equation, the same amount or ratio of elements can be found:
C + O2 --> CO2
This shows that the product will have the same ratio of reactants.
2. The original piece of wood and resulting ashes do not weight the same because the combustible parts of the wood were burned and converted to gases. This means that the missing mass is equal to the gases produced. The remaining ashes are the incombustible parts of the wood.