- No, it is not authoritative for the name which you asked for in the query. It is authoritative for one of the parent zones, though.
- Yes, it's authoritative for all names inside the zone that has been delegated to it (whether there are any records or not).
- Yes, if it's authoritative for
example.com it's also authoritative for
subdomain.example.com unless the latter has been delegated elsewhere.
It's important to note that your questions do not directly address the quoted definitions.
Your quoted definitions describe (a bit oversimplified) how the two types of nameservers operate overall, but your questions are about what type of answer a nameserver will be able to give for a particular query.
As I noted in my answer for question 1, that is a case where you are talking about a nameserver which operates as an authoritative server but which is not able to answer this specific query authoritatively (only returning authority information). This does not mean that this server is also your second category of server (one which honors recursion requests), it's merely that there is a bit of a mismatch between the questions and the definitions and that the definitions are a bit simplified.
To further complicate things, it is also possible to run a nameserver that operates as a mix of both types, but that doesn't seem immediately relevant to any of your questions.