I always used Comet and water to clean my Sharpmaker sticks, but it doesn’t seem to do as well on the WE super fines. I use the “Superaser” sold here by WE and it works pretty good. I think you can find it other places on the ‘net too.
As for when to clean ’em? I don’t let my ceramic stones get too clogged up; I’m afraid it’ll reach a point where it won’t clean up.
I have some 1/4″ diameter soft white Arkansas stones (used to be one, but I dropped it) which I chuck up in a cordless drill to sharpen serrated knives. I use the Superaser to scrub them clean while they’re spinning in the drill. Works great.