A few issues with the plugin repository configuration. When I tried to add a new repository, it didn't show up in the list until I closed and reopened GATE.
Also, even though I checked the enabled box on all of the repositories, the Available Updates and Available to Install tabs are disabled.
The tabs are disabled when User Plugin Directory is empty (as in the case shown on the picture).
The tabs are disabled, even though repositories are enabled, as you haven't yet configured a user plugin directory. Without a user plugin directory there is no where for the plugins to be installed to and so the tabs remain disabled.