The plateau itself is flat and pedestrianized, so yes once you’re up there. Getting up from the Gare with a suitcase is the problem — take bus 9 or the funicular from Pfaffenthal, don’t try the stairs from Grund unless you enjoy suffering.
Not on Place d’Armes. Try Am Tiirmschen on rue de l’Eau for Luxembourgish classics like Judd mat Gaardebounen, or Bouneweger Stuff for a lunch menu around USD 20. Reservations essential Thursday and Friday nights.
Live prices for every hotel and inn in the area — free cancellation, updated daily.