Is Kirk's middle initial R or T? Why did Starfleet forget the Romulans had a cloaking device 2 years after they saw it? Was it's Spock's ancestor or mother who was human? Is Spock Vulcan or Vulcanian? Were the Klingons conquered by the Federation, or just became allies?
It's "T", but Gary was referring to an old nickname he had for Kirk in school.
It was a new "improved" cloak they wanted intelligence on in Enterprise Incident. The original one was easy to track.
A mother IS an ancestor.
Vulcan and Vulcanian are interchangeable. Vulcanian fell out of favor because Vulcan is shorter and easier to say. See also "Englishman" and "Brit."