(1) The supermarket is in the north of the library; Xiaoming's home is in the southwest of the library; The library is in the southeast of the shopping center; The library is in the northeast of Xiaoming's home.
(2) The route from the school to the museum is: first walk 600 meters north to the library, and then walk 1000 meters northeast to the museum.
So the answer is: north, southwest, southeast, northeast;