Using carbon is personal preference. I usually limit it's use to removing medications. Some keepers do use it regularly though. If you choose to ... just make sure to change the insert on a regular basis (every 2-4 weeks...depending on
bio-load).
As far as the sponge and biomax bio-media ... yes, simply rinse them in used tank water to clean. Both will last quite awhile ... and the sponge itself will also colonize beneficial bacteria.
I also use an AquaClear 50 (200) on my 20g long. I use a piece of filter floss on the very bottom, followed by the sponge and 2 biomax inserts.