(1) The library is in the west of the school; The gymnasium is in the south of the school.

(2) To the east of the school is the Science and Technology Museum, and to the north is the Children's Palace.

(3) The library is in the east of Science and Technology City; The Science and Technology City is to the west of the library.

(4) The Children's Palace and the school are in the north of the gymnasium.

(5) There are schools and libraries in the west of Science and Technology City.

So the answers are: West, North, (1) West, South, (2) Science Museum, Children's Palace, (3) East, West, (4) North, (5) West, Library.