The growing of plants, burning of wood, and decomposition of living matter demonstrate how carbon can be in the at the same time.

The answer is biosphere, atmosphere and geosphere.
In the plants it exists in the form of macromolecules, so carbon is the part of the biosphere. By burning of wood, carbon is released into the atmosphere in the form of carbon dioxide. After the decomposition of living matter, carbon can be either released into the atmosphere or stored in the soil as the part of geosphere.

That is true tge cactus as a structural adaptation to its envirinment has it leaves reduced to spines. but this doesnt mean it cant produce food it produces food because of the presence of chlorophyll in its stem