How can I clean up from electrolysis?
The black one is probably $\ce{ZnFe2O4}$; insoluble compound of very weakly toxic metal ions, or $\ce{Fe3O4}$. The red one is $\ce{Fe2O3}$ In terms of disposal all above counts as non-toxic mineral materials, similar to sand.

It is also possible to have some carbon in this setup, but I doubt it.

Anyway, you have nothing too toxic in this setup, you can safely dump it into ground without any meaningful lasting environmental consequences.

The problem may arise, if the steel used was stainless steel or another iron alloy, but it doesn't seem to be the case from your description (and they are rarely galvanized anyway)