is it possible to have a different appIcon in the app itself and in the Store, based on the current language of the phone/store page?
No, It's not possible to have language specific Icons
neither in Store nor in Application.
If you want to detect current language of device you can use System.Threading.Thread.CurrentThread.CurrentCulture
or CultureInfo.CurrentUICulture
. But it's inside the application. So if you want to change any icon or image from inside Application in any of it's page, you can, but you can't change App Icon in the All Apps
section of phone.
Hope that helps..