2) If you were to always maintain backward compatibility, how is "depreciated" in any way an accurate term? If the old API continues to work indefinitely, its value stays the same.

If APIv3 has a `/foo` endpoint that is deprecated, usually I take that to mean that the developers discourage its use, and likely plan to remove it in a future version (say, APIv4 or APIv5). `/foo` will never be removed from APIv3, because that would be a breaking change, and so if I'm willing to stay on v3 forever, that's fine, but in the (likely) event I will want to take advantage of new features at some point in the future, I'm doing myself a disservice by using /foo because it will make the migration harder.

There is at least one case where I think "deprecated" is clearly, inarguably, the right word: when the developer wants to remove a part of an API (say, because it is a large maintenance burden), but it's also committed to stability, so they won't remove that api until some acceptably small number of users are using it.