Currently, we have to push to phabricator manually when we do changes to the phabricator repository. It would be great to have something which synchronizes these things automatically
This might be able to be configured through a Phabricator setting:
If you want Phabricator to host the master, you can add a URI with IO type of Mirror for your github repository under Manage Repository / URIs / Add New URI.
Phabricator will then automatically push to the mirror when new changes are committed. You will need to be careful with access to the GitHub repository though - if anyone pushes to GitHub, the changes will be lost, so if possible it should be read-only except for the user that Phabricator is authenticating as.