You should clean/rinse all the media using either de-chlorinated water or water taken straight from the tank. By rinsing the media in tank/de-chlorinated water, there is no risk of losing the beneficial bacteria.
The sponges will last indefinitely if they are cleaned regularly. If you allow them to become clogged with debris/detritus, the effectiveness of your filter will decrease dramatically and your water quality will suffer.
The carbon will lose its effectiveness, as chemical filtration, within about a week. And, carbon is not at all essential in your filter; many people only run carbon to remove medications or to 'polish' the water. You can run carbon all the time, if you prefer, but it will be expensive and last only a few days.