Decomposers as you said break down dead plants and such, after that. The animal or plant turns into recycled materials that feed other organisms. They then release carbon dioxide into the air.
Decomposers mine them from the dead so that these recycled materials can feed the living. In the carbon cycle, decomposers break down dead material from plants and other organisms and release carbon dioxide into the atmosphere, where it's available to plants for photosynthesis
abiotic factors are factors that are not organ or biotic as one would say like the nevirmwnt or air or water biotic factors are things like tress food plants ect