i have try to install elgg root it install it always on subfolder , and when i go to the elgg instaled directori there is no graphic same thing whit joomla and last if i upload files to my public _html when someone goes to my domain can see folders and stuff.
If you want elgg as the main site, you can move the contents in the folder from the sub-directory to the public_html one.
The reason they can see the stuff is because right now you don't have a index.php or index.html file in the public_html folder. The servers' default behavior if there is no index page is to show a folders directories.