Well, maybe I don't get it properly. Valves 4 and 7 are spigots, the rest are ball valves (as shown in the picture, I think).
To do nothing, close all valves.
To move fresh water to the salt/mix vessel, you open 6, 3, 2, and energize the pump in the bottom of the fresh vessel.
To move fresh water to the ATO, you open 6, 7 and energize the pump in the bottom of the fresh vessel.
To move salt water to the sump, you open 5, 7, and energize the pump in the bottom of the SW vessel.
To agitate the salt/mix vessel, you open 5, 3, 2, and energize the pump in the bottom of the SW vessel.
What's the spigot #4 for?
Did I get this all correct??