The term "authoritative" used for dns lookups translates to "in charge". This means that when you receive a response from a DNS server and it contains the sentence "Non-Authoritative" in the answer portion of your request, the DNS server is telling you " here's your answer, but note that I am not charge for the domain you just looked up"
To help illustrate this and clear your doubts, I've requested below, information on Firewall.cx from two DNS server, one from my ISP and the other being the DNS server in charge of the domain, note the response from each:
> server ns1.otenet.gr
Default Server: ns1.otenet.gr
As you can see, the first server, ns1.otenet.gr appended the "non-authoritative answer" sentence to its answer, while the 2nd server, which also happens to be in charge of the domain, didn't include such information in its answer - showing that it's the authoritative server for the domain in question.
Coming to the 2nd part of your question, T1 and E1 lines are digital lines used in WANs.
Basically T1 and E1 are pretty much the same because the T1 term is used in the US Canada and Japan, while E1 is the term for Europe. They describe the same type of digital carriersm with small differences between them.
A T1 line has a speed of 1.544 Mbps (24 x 64Kbps channels) and uses copper wire as a medium, whereas E1 has a speed of 2.048 Mbps (32 x 64Kbps channels).
The reason E1 has a higher capacity compared to T1 is because of the way it encodes the digital signal, but that's a different topic and story altogether.