The archived schedules have moved to the CS Education Research wiki.
New! Apparently there are reasonably RESTful APIs to various runtime things.
Some reference code that uses them: API client library. Look at the integration tests in blob/master/edx_api/integration_test.py
These are separate from (eg) the XBlock runtime environment.
Use LTI to embed an iframe to your app with identity assertion (in other words, ask edX to embed your tool and pass you some user info). Links below are in the order I would have liked to be presented to understand what this is and how to use it.
This section deals with features and functionality which can only be added by manipulating the xml backbone of a course. The workflow for making changes would be something like: export course from studio → edit xml of exported course → reimport into studio
These features and their creation and formatting are discussed in studio documentation
The following functionality is not covered in official documentation, use at your own risk edX's documentation of course xml structure