Is there a complete reference manual of all the commands accessible from, for example, curl? I want to get a JSON list of all my items in my favorites, playlists, etc.
Most likely not, best you can do is to look at the sources.
Im in middle of documenting the apis with javadoc commenting the methods clients can call, hopyfully once its done it could be accepted as pull request.
Have a look at API Overview - Volumio Documentation