I don't clean my rings. Sometimes they get a swish in the bucket of tank water, but that's it. I always keep extra bags of them in all my HOBs to quick cycle a new tank. And yes, I keep them on top of my sponges.
How often you should clean your sponges depends a lot on your fish load. In my BN grow out tank, I clean it weekly. In my goby tank, monthly. Cichlid tank has two filters, so I rotate them bi-weekly, endler tank, monthly...etc. etc. When it gets really gunky and slimy, give it a rinse.