Not this set specifically, but I sharpen all my knives with Arkansas stones. Dish soap and water will clean the stones.
Some folks prefer to use the stones dry, others will use a handful of water on the stone while sharpening, and some prefer to use a thin coat of oil. If you use oil, use a food-safe mineral oil, since those are your kitchen knives. It will work fine. You may need to reflatten them eventually... but it will be years. Wouldn't worry too much about that unless they're noticeably bowled.