Yes it stopps. Everytime I press ctrl + 12 to open the GSX popup Window I see the same textline is coming back to the top of the 3D-Window of FSX that shows: "[GSX] Regeneratin airport cache (49 %), please wait..."
No, it doesn't. 49% doesn't mean much, it might be 49% of a long process or a very short one, depending if there are many new sceneries to be updated or not.
But your issue is the program can't write to the cache folder ( C:\ProgramData\Virtuali ), because you have a permission problem so, it's not that it has stopped, it never began in the first place.
I have deinstalled GSX completely once more. I have rebooted the system. I have defragged the registry database, rebooted the system once more and reinstalled GSX using the newest completeinstaller of GSX from your homepage. The same problem.
I don't understand why you keep doing different things to what I've asked. I haven't said anything about defragging the registry, rebooting Windows, etc. If the problem had anything to do with the registry, I would have told you so.
I had deleted the virtuali\couatl folder as you described it, after that I created them via folder programdata right click --> new --> folder. Both folders, the virtuali and the subfolder couatl, are empty.
If it's empty, then try to remove the whole "Virtuali" folder, and recreate it manually, then try again.
Don't do anything else that I haven't explicitly said to do. Just do this, and launch FSX (with GSX installed, obviously)