Sounds like you didn't just publish the system action, but saved a copy. You can not publish a system action by editing it. That will save a copy as the button directly states on the toolbar. You have to publish from the list view. Navigate to CB Auto Actions > Auto Actions and delete your copy (or copies). Next navigate to CB Auto Actions > System Actions and publish the "CB Gallery - Comments" system action by clicking the red x in the Published column (or selecting its checkbox and clicking Publish on the toolbar).

Can I include a link to the gallery item?

You can construct a URL to a single media entry using the below URL structure.

Fullsize:
index.php?option=com_comprofiler&view=pluginclass&plugin=cbgallery&action=item&id=MEDIA_ID_HERE

Thumbnail:
index.php?option=com_comprofiler&view=pluginclass&plugin=cbgallery&action=item&func=preview&id=MEDIA_ID_HERE

Replace MEDIA_ID_HERE with whatever substitution is necessary based off whatever trigger you're using.

I'm not sure why you want to do this though. Latest CB Activity, CB Gallery, and CB Auto Action releases installed you can have all of this using onsite notifications by simply toggling the necessary system actions on.

Where do my members see 'onsite notifications' ?

If enabled in CB Activity > Parameters > General there will be a globe icon top right of the CB Menu bar at the top of their profile. You can also output this globe as a module or anywhere that Joomla content prepare is supported.