Which is the best way to remove everything that was created during the installation process by the FSDT installer / GSX Pro MSFS, so everything is the same as before the installation?
There's no need to do anything like that, it's way easier: if you choose Uninstall from the FSDT Installer and reply Yes only to the first question (Unlink) but No to the 2nd question (Uninstall), the two links in Community folder will be removed, so you can keep the program installed in its own folder but, for all intent an purposes, in MSFS, it will be exactly as if GSX was never installed to begin with. GSX Pro will just take space on its own folder, but as far MSFS is concerned, it doesn't exist anyore.
I noticed for instance that in the Windows System I have no entries for the deinstallation of GSX Pro MSFS (only for FSDT airports that I bought for FSX and Prepar3D).
Not sure why you want in the "Windows System" (not sure what that means, exactly, you mean the Windows\System folder?), if you wanted to uninstall the "
Fsdreamteam Universal Installer" itself, like any standard Windows program, it's uninstalled from the "Programs and Features" section of the Windows Control Panel.
Doing this won't make any difference to your MSFS installation. As I've said, as far MSFS is concerned, GSX Pro will be completely ignored, as long its two packages are not visible in the Community folder so, uninstalling the FSDT Universal Installer will only be useful if you suspect issues with the Installer ITSELF, like installer crashing, not downloading, activations not working.
I launch MSFS as an administrator, then when it starts the loading process I wait a while (well before the Main Menue appears) and launch also Couatl GSX MSFS manually (also as administrator?). I guess this is the procedure you follow. After the main menue appears, I select the flight (or activity) normally.
This shouldn't even be required. GSX Pro works perfectly fine, and this is how we test it, with MSFS starting normally, and GSX Pro starting automatically.
However, this assumes your Windows user account is NOT "limited", meaning it can use Admin permissions if required. Is this your case? Because, if your Windows account is in fact Limited, you might need to run both As Administrator, but if you use you PC mainly for simulation, it would be much better to just give your user account admin permissions.
If, instead, your Windows user account already has admin permissions, then it's completely useless to run MSFS and Couatl64_MSFS.exe as Admin.