Yes. The Biowheel is more of a gimmick than anything else IMO. It works, but not any better than any other biological media (like the ceramic rings in the Aquaclear filters). All it does is provide surface area for bacteria to colonize. As long as water is moving through it, beneficial bacteria will grow on it. That said, do you have any idea why it isn't turning? You never want to clean the Biowheel itself, but you can clean the pegs on either side of it, and also clean the slots in the filter where the pegs sit. That's helped every time for me.
You can stuff whatever media you want inside the cartridge, but IMO it's probably more trouble than it's worth. Carbon leaching toxins into the water is a myth that seems to be perpetuated by companies and retailers that want you to replace it often. There's money to be made that way.

I've personally had Emperor cartridges (same thing as Penguin cartridges) that I've run for over a year. I swished them out in tank water to clean them until they started to fall apart. I never took the carbon out, and guess what... no ill effects whatsoever.