Biomass combustion processes may be controlled to intentionally generate a carbon-containing ash, from which activated carbon is produced according to the methods disclosed. Some variations provide an economically attractive process for producing an activated carbon product, the process comprising combusting a carbon-containing feedstock to generate energy, combustion products, and ash, wherein the ash contains at least 10 wt % carbon; separating and recovering carbon contained in said ash; and further activating or treating the separated carbon, to generate an activated carbon product. Many process variations are disclosed, and uses for the activated carbon product are disclosed.