He's done a good job with the label maker.
Follow the flow, through the valve, follow the handle.
For example your second picture: Maindrain/Skimmer: the valve is in the null position, your pump is sucking evenly from both of them. The blank off is on the opposite side of the handle.
Then when you follow it: It's drawing from the pool but not from the spa, and it goes into the pump. On the other side of the pump (where it exits), the water is under pressure. The hose bib is there if you'd like to drain out some water.
Then it goes to the filter (labeled "inlet"). The valve there is closed so it must go through the filter. Not sure where the pipe goes. But keep that valve closed if you want to filter the water.
Out of the filter (bottom pipe), to the heater, input on top, out the heater on the bottom, through a check valve, to the returns.
The return valve is set so all the water goes to the Pool, not the spa.
Then the water features look to be electically actuated. (Can't tell the settings), through your puck clorinator.