Regarding question 1: No, not always. Some nameservers will do recursive queries for you, but some only provide answers for zones for which they are authoritative. The global root servers work this way, for instance. Public DNS servers like 22.214.171.124 will do recursive queries for you, however.
Regarding question 2: An authoritative server for a zone is one that has responsibility for the zone, yes. It either knows all information about names in the zone, or it delegates authority about sections of the zone to other servers. For example, ask a root server for an SOA record for
example.com and it will provide a list of nameservers for
com. Ask one of those servers about
example.com and it will provide a list of servers for
example.com. Ask one of those servers, and it will provide the SOA record, letting you know that the server is authoritative for the zone, and you can then query that server about names within the zone.