Hi,
You are right in that the API documentation is severely lacking, and you're on the right lines about where you're looking. Personally, I found it easier to use Chrome's developer tools to analyse the requests and responses made by the web interface (which still uses the API), then augmenting that with browsing the source.
I'm hoping to contribute some stuff on the API to the documentation once I get a bit more time. If you do have any specific questions on parts of the API though, I'd be happy to try and answer them (though I'm far from a definitive authority on it).