Soaked as long as you would for sharpening? At least!
80, 100, 120 are okay. 80 is the fastest, obviously. 150 and 220 are a little slow, but fast enough to start the lapping process. It's not necessary to lap with screen though.
Some people lap with naguras or compound, but I lap by rubbing the flattened stone against the other stones, all the way through my set's progression until the next finer stone in my set. So, I rub the flatten the 400 and rub it against the 1200. Flatten the 1200 and lap it on the 400 and 3000, etc.
BDL