I have 2 questions about the Original Broadway Sweeney Todd...?

If they needed grooves in the floor, chances are they would tour a false floor which is placed over the stage proper in each venue. It raises the stage slightly, but it means that the floor is correct without having to make a mess of the floor wherever they go, and is a pretty common solution. I worked on a production of Les Mis where the floor had "railroad tracks" on it - tracks which guided the barricades and other set pieces, and we had a false floor (we also had a revolve which needed a false floor, but that's irrelevant!).