Ok you kind of confused me here....
Sorry about that. To cut the story short, GSX is now working. That means that the proposed path from the installer works well: C:\Program Files (x86)\Addon Manager. During installation the pathes to the commuity folder will be set automatically.
This is the way I start the GSX:
1) Starting MSFS, selecting plane and gate with are working which GSX
2) Starting FSDT Installer with the shortcut from the desktop with administrator rights (rightklick on shortcut)
3) Starting Start Couatl for GSX MSFS with the shortcut from the desktop with administrator rights
Following this steps, GSX is working as previewed.
Thank you for your help finding a solution!
Kind regards