(1) The gymnasium is in the west of the Science and Technology Museum and in the east of Xiaoming's home.

(2) The Panda Pavilion is in the east of Xiaoming's home, and Xinghua Primary School is in the northeast of the gymnasium.

(3) Xiaoming goes west to the library, south to the gym and west to go home after school every day.

Just finished: west, east; East and northeast; West, south, west.