And for me, that means no icon is ever to occupy a permanent spot on my screen, be that on the desktop or the taskbar. Bertel ...

At the bottom, you'll see Show desktop icons. If it isn't enabled already, that's the reason icons have disappeared from your Windows 10 desktop. Disable Windows 10 Tablet mode.

To change an individual desktop icon, right-click the shortcut icon, select "Properties," and navigate to the "Shortcut" tab. Click "Change Icon," then browse through the available icons.