One question at a time:
Are /user/index.json?name=RaisingK and /user/index.json?id=13506 supposed to work? I figured out /users.json?search[name_matches]=RaisingK but what about searching by ID? I tried six variations based on the name one, but I either got Failbooru or a search-less listing...
Or maybe I tried it at a bad time--now everything is Failbooru...