Because of common sense i also set IsWindowed = false when calling Device.CreateWithSwapChain().
This combination caused the mouse cursor to stay visible after alt-tab and reactivating the app.
But when you change one thing: call Device.CreateWithSwapChain() with IsWindowed = true; this Cursor problem doesn't happen anymore. You start DirectX windowed but my AppActivated eventhandler above is triggered at startup too, so I get a fullscreen immediately at startup.
So, now I have a fullscreen app, that never becomes windowed and never shows the windows mouse cursor, finally
If any expert can explain this difference, I'm happy to listen, but for now I'l just accept it