Depending on requirements given to you, but mostly no as the list of the variables would make it too long.
However I know a professor at university that demanded all variables to be listed too...

The class diagram should show only the externally visible characteristics of the class. Attributes (RW/RO/WO) correspond either to non-private variables, or to conventional non-private accessor methods. Private variables would not normally be shown, although you sometimes see one included because it's important to the reader's understanding of how the class works.

since it is a static structure I don't think you are allowed to do that

do what?

how to create a class diagram?

By using common sense. Class diagram represent all the method provided by the class and global variable used (not always required). Then you connect classes between each other depending on their availability. If this is not enough read here