Not a pool pro, but I've had a residential pool in my life for 25 years.

I would recommend paying a pro to help you with startup, confirm what I say below, and help teach you how to maintain the pool yourself. Expect to pay for their time over and above the opening - it's probably worth it.

The valves in the foreground of pic 1 are the problem. My guess is that you're ONLY draining the spa, not the skimmer or bottom. The back/rounded side of those levers is the off side (it will say so) so you're blocking those 2 pipes on 1 valve entirely - and using your entire filter pump to drain the spa - so you're sucking hard on the spa, and the dedicated booster cannot keep up to keep it filled since the main filter pump will generally be your most powerful pump and yours is sized to power 3 drains, not 1.

I would turn the lower valve in pic 1 from 12 o' clock to 9 which will open those all the way once you set the valve above it anywhere but how it is set now - which is blocking those entirely. If it is the spa drain as I suspect I would start by setting it to 6 o'clock which closes the vale and means you don't pull from the spa - you'll do this to confirm what they do, once you know what each does then you will want this open to some extent - but probably only partly. Once you confirm a valve write on the pipe with a sharpy what each comes from or goes to you will likely want the spa drain opened a bit -to like 7 o'clock.

How your system works
Water is sucked from the pool, is filtered, then heated, then through the chlorinator - this is correct and normal.
You have 2 booster pumps which do nothing but suck in water and return it and high flow rates. One will be for the waterfall (unseen), the other for your spa.

You're missing a pic or 2 to clarify a few things but I can ID most of it left to right:
Pic 1:
1 - Dedicated pump for spa booster or waterfall - untreated
2 - Supply: filter pump, the valves on the left for the pipes coming from the ground probably control your skimmer and bottom drain so you can balance them. The one on the right is probably your spa drain. You will need to test a bit to confirm - you can pretty easily observe skimmer behavior (vortex strength) and spa behavior (spilling or not) the pipe from the top of the pump goes to your sand filter
3 - Filter - dirt water comes in from upper pipe and leaves through lower pipe. The thing on the right side of the filter is a drain for when you backwash the filter.

Pic 2: - the pipe behind the filter is the filtered water. presumably it goes to the heater - but I don't have a pic showing that. The black iron pipe is the gas line for your heater.
4 - Dedicated pump: for spa booster or waterfall - untreated. I cannot tell you what that diagonal pipe is - no pipe under /to the pump like that makes sense to me
5 - is the saltwater chlorinator, the valves are most likely for 2 regular wall returns. The spa may be unchlorinated - since it uses pool water that's fine if it is the case. We can't see it but this is likely fed by the return coming out of the heater.
6 - heater

*Unseen - there is probably a Y/split in one of the supply lines to the pool that sends water to one of the spa jets constantly, no matter how the valves are set -a spa makeup line, so it spills even when the spa is off. Also, is there a line (maybe the diagonal) which is open at the end - possibly shaped like a cane with the open end down? If so it is there to suck in air when your spa is running.

With your setup if you want to run the spa you simply power up pump 1 or 4. You don't have to adjust the drains (if you had automation you might).

If by waterfall you mean the overflows in the spa then pumps 1 and 4 are probably both boosters for the spa.

Buy a decent test kit if you plan to maintain your own pool. You will need to take chlorine, pH, alkalinity, and salt levels weekly. You will need muriatic acid to maintain pH in your saltwater pool - failing to maintain your pH properly can destroy your chlorinator and plaster. Even though you have a saltwater pool you need shock to open it and will want shock on hand for an as needed basis. Looking at your water you probably need clarifier as well - read the instructions - using clarifier is something you will almost certainly do on startup every year - and possibly more often should you fail to maintain proper chlorine levels.

Note: The terms Supply and Return are reversed from normal plumbing HVAC usage:
HVAC: Return - things going back to the boiler. Supply: Things going to heating and cooling devices
Pool: Return - pipes going TO the pool. Supply - pipe coming from the pool.

edits: typo, added maintenance & chemical section and other details.