No, they are not because they are stored in custom object properties. I don't think Blender has a native way to store gizmos in scenes.

Yes, go to the location where the addon is installed, and copy one of the file in the Gizmos/ directory. If you've already coded a Blender gizmo, you'll recognize what is in these files, and the extra info for LilyGizmos at the beginning are quite straightforward.