Yes true. The G-Droid apk can also be downloaded from here https://f-droid.org/en/packages/org.gdroid.gdroid/
G-Droid can do unattended installation (and uninstalls in version 0.7.1) on rooted phones. It will ask you. There is also a setting to allow root to be used
In the my-apps tab there is also a button to 'update all' which work well with root permissions. Without root each update installation requires 2 more clicks
But no, there is no service yet to check for updates automatically and then install them automatically
Server run by the main developers of the project It is not focused on any particular niche interest - everyone is welcome as long as you follow our code of conduct!