There is probably 2 intake lines, one from the bottom drain, and another from the skimmer. You definitely need valves on those so you can choose to pull all your suction from the bottom if it's really cloudy, or the top if it's pollen season.
Then there is likely 2 discharge lines, and you can have, but don't absolutley need valves on those. The water will go back to the pool as long as the lines aren't obstructed. Tehre should be a 5th line somewhere, the waste line, where the water goes when you backwash. there may be no line, it may just dump, or there could be a blue hose rolled up that the waste water splashes out of.
You know your stuff. Holy cow! I have a lot to learn. I hope it's not as complicated as it sounds.
I have a call in to the pool guy, he gaves us an estimate at inspection for the valves and we need to repair a small rip in the liner. Hopefully, he'll give us a quick crash course.
Thanks so much for your help.
When do you open or close those lines?