I use a very mild solution of pure bleach.. but for beginners, I would recommend ammonia, meth blue, malachyte green or aquarium medications. In my experience, first time anyone uses bleach, they overdose on it and the equipment needs to be thrown away because of that.
No, I do not usually use airstones, the water which is coming from the aquarium will have oxygen in it. If there are a lot of fish or large fish, I will use an airstone.
