If I am writing the client and server code, the server code is quicker to check than documentation.
Never saw the need for API testing if I am the user of the API.
It does indeed have a standardized format.
Non-cookie auth is actually handled in some of my projects with about a dozen lines of a header parser that then passes it to Django sessions.
Pagination in my latest project is handled as date filters or done client side. Way faster for the user that way and removes a lot of PITA.
Throttling is handled by other bits of infrastructure. If you do that inside a Django view or middleware you are likely doing it wrong.