Whale blubber was melted down and used as oil in lamps as far back as the 1700s, but it was very expensive. In the 19th century, cheaper oils such as kerosene (or naptha, as it is known in Lyra's world) replaced whale blubber as lamp oil.
The Regius Professorships are "royal" professorships at the ancient universities of Britain.
However Gloucester, in our world, is not one of the ancient universities. The University of Gloucestershire was established in 2001.
A popinjay is a British woodpecker, specifically the green woodpecker.
However the word is also used to describe someone vain, self-important or vapid, as here.
Microcosm and macrocosm is the idea that the same patterns are reproduced at all levels of nature, from the largest scale (the macrocosm) to the smallest (the microcosm).
Fire hurlers seem to be a cross between a cannon and a flame thrower that is regularly used as a weapon by the bears, and they make a reappearence later in the trilogy.
Polar bears in our own world are also nursed by their mothers until they reach about two and a half years.
Female polar bears are noted for their affection towards, and fierce defence of, their cubs.
The fight between the two bear kings is vicious and violent in Northern Lights, as is a fight between real polar bears.