API is more general term for programming interface whose function is not nessecarilly obtaining data. (it could also be updating or deleting data). this .data TLD as i understand would be just for obtaining data from website in structured way. for example if google had .data domain it would be something like this : you enter google.data?search=lady+gagga and it will return you page in json or some other format for results of that google search.
Yes. Also, almost all APIs are designed around small bits of user or query data, just like your example.
This seems more intended for bulk data, which is likely going to be some pregenerated chunk in the MB, GB, TB range and so less suited to the JSON API call paradigm, and more likely to involve a simple lookup to disk rather than being computed on the fly from some database.
