With the air pump, let it go as long as you like. An inline filter is important.
When I use the pump, I run it until foam comes out of the fermenter.
I'll second all that. At least with my setup, it's pretty obvious when the wort is getting close to saturation - for a few minutes, almost no bubbles make it to the surface, but at around 10 min it's climbing out of the bucket.
Alright can someone explain the importance of the stainless steel stone?
It doesn't have to be stainless; I use the cheap plastic ones from the pet shop and just throw them out every couple batches. The important thing is that it can be sanitized.