401 is not really an error but uthentificatiob prompt. When a browser or other http/webdav client see the 401 status code it will ask a user for credentials and then send them in header Authorization: Basic user:pass.So when you disabled authorization the problem was "solved". Turn the authorization back!
The 405 error means that a server doesn't allow to make the operation (http method). In your case it rejected MKCOL request i.e. an attempt to create a folder.This is probably because you disabled auth and the server doesn't allow editing.Also note that you may have auth in both nginx proxy and apache webdav.
