What if a portion of it burns away? ;-)
Most organic materials produce CO and/or CO2 as a byproduct of combustion, IIRC...
Another good question.
Burning does not alter the ratios of carbon isotopes... unless they are not uniformly distributed in the carbon and one isotope is more prevalent in the burned area. Since this is generally not the case, carbon isotopes are pretty much mixed homogeneously, unless it can be demonstrated that one area has been irradiated more than the other. All things being equal, the CO and CO2 byproducts of combustion would be composed of carbon isotopes in the same ratio as the original material that was burned. The residue of the original would still have the same ratio.