(1) The school is in the southeast of the park, northeast of Xiaoming's home.

(2) The gymnasium is in the northwest of the library, and the library is in the northeast of the supermarket.

(3) There are three ways to get from Xiao Ming's home to the library:

That is, the distance from home to the park, to the stadium and finally to the library is: 400+260+300=960 (meters);

The distance from home to school and then to the library is: 300+280=580 (meters);

The distance from home to the supermarket and then to the library is: 450+480=930 (meters);

Among them: from home to school to the library; It is the farthest from home to the park, then to the stadium and finally to the library.

So the answers are: southeast, northeast, northwest, northeast.