As far as I know, the program accesses to the Internet only at lauch time with Java Web Start version to check if an update is available.
Cut temporarily your access to the Internet and you'll see that it still works! [;)]

How do people put in green grass, trees, sky and clouds?

Grass and sky comes from textures you can set with the dialog box shown by 3D view > Modify 3D view menu item. Trees come from additional 3D models imported in the program from here or there. Please read user's guide and included help for more information about this feature.