Thinkup, in your first post starting the thread you said you were doing this as a guide for the future to help others.
With that in mind, some constructive criticism.
You should not have a prefilter in front of your backwashed AN filter. You do not want to restruct/reduce water flow to the AN filter in any way. If you do, you will cause incomplete backwash and that will kill the mineral.
You should not install a by pass around this equipment. You have by pass valves on both pieces and that is all that is needed. To remove the filter or softener if ever needed, you disconnect the control valve from the by pass vale after putting the unit in by pass.
You should not plumb the AN filter back in that corner. The way it is now will make adding mineral difficult to impossible and looking at the top dome hole plug location, you'll have to remove the filter from the by pass valve, and loosen the control valve to get the plug out and new mineral into the tank. I would have put the AN filter next to the main water line as you had it in your first picture in this thread; main, and to its RIGHT the filter and then the softener.
I would shorten all the lengths of plumbing. There is no need to go so hig above 'things' or out from the wall as much as you have it.
I would have installed both pieces back closer to the wall. And I would have used the Clack elbow plumbing connectors instead of the brass and then copper pigtails you had to buy, cut and solder straight out the back pf the bu pass valve. Instead of PEX, I would have used 3/4" CPVC or copper.
You do not want check valves in the drain line. T the softener drain line into the the run of 3/4" PVC from the AN filter. Both control valves have internal valves for the drain line flow, so the drain water from one can't get into the other control valve. Plus you set the time of day on the filter ahead by 45 minutes so it backwashes before the softener regenerates so neither unit is using water while the other is using water anyway.