Given that rels are established to be 1.2 seconds in Evolution of the Daleks (2007), the "9376 rels" are approximately equivalent to 3 hours, 7 minutes and 31 seconds, answering The Doctor's question.
In common with the season opener, The Woman Who Fell to Earth (2018), there are no opening credits or title sequence.
The second New Year's special, with the first being The End of Time: Part Two (2010), which aired on January 1, 2010.
The creature's nature appears to be based on The Puppet Masters, a 1951 novel by Robert A. Heinlein. This novel predated the similar movies Invaders from Mars (1953) and Invasion of the Body Snatchers (1956) (and even Jack Finney's 1954 Body Snatchers novel). It was unofficially adapted as The Brain Eaters (1958) and Operation -- Annihilate! (1967), before being officially adapted as The Puppet Masters (1994).
Titled "Resolution" as a reference to the fact it is a New Year's special, rather than the traditional Christmas special.