I don't run carbon at all, but that needs to be replaced otherwise the carbon loses its effectiveness and it essentially just becomes a place for more bacteria.
Any bio media, sponges, floss, etc. just gets swished. But if any does need to be replaced I wouldn't do all three at the same time.
The brown looks like diatoms, which is the common algae to have in new or newly established tanks for whatever reason.
The fuzzy stuff could be a type of hair algae. How long are the lights on?
Good luck with the cpds.