Sun and Moon
You can disable the sun or moon by using the display settings drop down on the Map and 3D pages. Toggle the display on/off by clicking the switch control. If you have a PRO subscription, you can also enable/disable display of the Galactic Center (the center of the Milky Way) and Meteor showers.
Note: currently, the Meteor setting only affects the 3D Sphere view. Meteor showers are not displayed on the Map.
Main Display
The display options control above the map to the right (highlighted below) allows you to configure what is shown. Here are the four possible configurations:
1) Map, Timeline + Altitude Chart
2) Map + Altitude Chart only
3) Map + Timeline only
4) Map only
Full Screen
Irrespective of the display mode selected above, you can always toggle full screen on/off. When enabled, the header and footer are hidden to maximize screen real estate for the map: