Dana, well, you've got a bit of a situation here on the forum in that you've started two threads about essentially the same topic, and you've now got multiple people chiming in, some of whom have pinged others to join in. Maybe a mod will choose to straighten that out (
@mknauss?). This is what I see and what I would do.

The short of it is, your system was not properly plumbed. It's likely a DIY job by some previous owner that got it to work. And your last pool guy somehow figured it out. I suppose you could try the same, you have been, but you've got several issues that a replumb could solve, the two biggest are that your system is too confusing to use, and that there are some built in hazards to your pump (your pump can be blocked on both the suction side and the pressure side) if someone turns a valve or two the wrong way.
I'm making a few assumptions. That by "union" you meant "tee" and that your pool equipment is not located lower than your pool (the only reason I can think of for valves A and B to remain), and that A and B are fed by two skimmers. So...
Valves A and B shouldn't exist. That should have been a single three-way valve, that you could use to balance your skimmers. As a three-way, it would allow any amount of flow from either skimmer, but would never allow both skimmers to be closed off at the same time (which protects your pump). "Union" F would go away. Plus, ball valves are prone to failure and shouldn't be used in outdoor pool plumbing.
Valves C and D shouldn't exist either. I can think of no reason you'd want to isolate your panels with those, but a few reasons you should never. Either of those valves closed could block the output of your pump. That's bad. And both closed would block your panels from properly draining after use, or possibly damage them by trapping super-heated or frozen water, either of which is not gonna end well. Consider what expansion and contraction will do to panels and plumbing up on the roof with both valves closed! Until you get this fixed, never close either of those valves.
Union G and valve E are in the wrong place. And your system is missing a check valve. Refer to the drawings I linked. That's how your system needs to be replumbed. This is what's causing most of your confusion. If the three-way (E) was where it should be, in place of union G, the controller could do it's job (turning solar on and off) and E could also be used to bypass some of your pump's flow to the panels (in case your one-speed's flow rate is too much for your panels). The missing check valve and union G should be located
after the panels.
Other considerations: three-way E needs to be a special type of valve, known as a "Solar Drain Down." That type of valve functions as a normal three-way when the pump is running, but with pump off the drain-down feature allows both ends of your solar plumbing to drain out all the water. This prevents super-heating and freezing, as the panels should be virtually empty of water when not in use, especially in the winter. If E is not a drain down valve, it should be replaced with one. And if it's salvageable could be used in front of the pump, to replace A and B.
There needs to be a vacuum breaker in the system. Is there? Sometimes it is on the roof, but it can also be near the pad. Generally it needs to be some number of feet above ground (six or so, I think). That breaker allows air into the panels when the pump is off so they can properly drain.
There are a couple of make-shift ways to determine the proper amount of flow through your panels. The manufacturer might be able to provide you with the proper amount. With E where it should be, you could adjust the flow to the panels to achieve the proper amount. It probably is doing that now, as you say one position is "halfway." You can sort'a calculate the amount of flow, using math and perhaps the pressure gauge? I don't know how to do that. Other "old timers" can judge the proper flow by feeling how warm the return water gets. Too hot, and the flow is too low, etc. I wanted to optimize my panels, so I installed a FlowVis. My panels' manufacturer spec's 40GPH, and that's exactly what mine get. I adjust flow to them using my variable speed pump while viewing the FlowVis flow meter. With a single speed pump you'd use valve E and the meter.
So here's my recommendation, then I gots to get to work. Do this right. Let go of trying to figure out what you've got. Hire a qualified plumber, ideally from a solar heater installation company, to come out and replumb your pad. He'll know exactly what to do, and bang it out. Bite the bullet and spring for whatever new parts you don't have. Have him get rid of the parts you don't need. If you purchase a FlowVis flow meter, they function as a check valve. So if you used that for your missing check valve, you could dial in the flow to the panels precisely using valve E (or it's replacement if E is not a drain-down valve).
It might be only a few hundred dollars for parts, and maybe that much more for the plumber. For that dough your system would be entirely foolproof in terms of protecting your new pump, and be soooo much easier to use,
and remember how to use. For both you and others in your household, and for the next owner.
If you instead want to continue down the path of figuring out how to use what you have, then others in your other thread can help you with that. Good luck either way.