I've always sort of thought of the Third Reich as an attempt to rebuild the Holy Roman Empire plus the Prussian territories. The First and Second Reichs kind of combined I guess. The conquests like Poland and Ukraine I always figured were planned to be administered more along the lines of colonies or with military governments for an undetermined amount of time. It's interesting they considered the Dutch as Germans since they had not even been formally part of the HRE since Westphalia and really split off much earlier than that. Makes me wonder what they planned for the Scandinavians.
Not much, I´m afraid. The term "Third Reich" is purely historiographical; the Nazis themselves simply called it "the Reich". Other than the fact that there had been a Holy Roman and a German empire before, there isn´t really any relation ideologically speaking, since it resulted from Hitler´s coup d´état. Furthemore, the Nazi idea of "German" was racial (instead of linguistical, as it should be), but then Nazi ideology never had a yota of understanding of science (and technology) anyway.