In ATDD you start with writing tests to represent the requirement. Since you start with this, there is no production code to satisfy the test which is why the tests will fail.

There is no hardening sprint, there are only regular sprints. If it's an ever recurring non-functional requirement, it can be added to the definition of done. If it's not it can be added (as a criteria) in the product backlog (item).

if the documentation is adding to the quality and maintenance of the software this is definitely a good argument for documenting every sprint. Just because that's the way it's done and we don't want change is not a good reason. Tooling that requires is also isn't. And the scrum master cannot demand this kind of things. If the company's definition of done says so, you must :)

Self management is important. All the other options the scrum master takes a decision by himself, it is better if the solution comes from the development team.