IF you have any adminatrative questions, I'm not able to help you, as I do not live in Luxemburg.
If you are in doubt if it's worthwhile to have a bike while in Luxemburg, I can only say YES IT IS!
I live some 100k from the border with Luxemburg and it's one of my favorite
places for day and weekend tours, ever since my elder brother showed me around in 1984.
Got my licence on thursday, saterday he told me: Now you have a licence, w'll learn you how to ride...