Short answers, pulled from the story.
Canon in fiction refers to the body of works set in a particular fictional world that are widely considered official or authoritative, especially those created by the original author or developer. A canonical story is one whose events, characters, and continuity are treated as real within that fictional universe.
During George Lucas's ownership, canon was structured in tiers tracked by Lucasfilm creative executive Leland Chee, with theatrical films and Lucas's own statements at the top. After Disney's acquisition, Lucasfilm designated all Expanded Universe material published before the 25th of April 2014 as non-canonical "Legends," with new canonical material overseen by the Lucasfilm Story Group.
The official Star Trek website defines canon as the events that take place within the episodes and movies, meaning the live-action television series and films. Tie-in novels, comic books, and video games are explicitly excluded, though the site acknowledges that elements from those sources have occasionally been introduced into the television series.
Fanon is a portmanteau of "fan" and "canon" that describes ideas or interpretations widely accepted within fan communities but carrying no official status. Fan fiction is never regarded as canonical, though fanon may describe either a shared community interpretation or a single fan's personal reading of a fictional universe.
Yes. Estates have approved continuation novels that the original writer never sanctioned, including Scarlett (1991) as a sequel to Gone with the Wind, The Time Ships (1995) and The Massacre of Mankind (2017) as H. G. Wells sequels authorised by his estate, and The Monogram Murders (2014) by Sophie Hannah as a Hercule Poirot sequel authorised by the Agatha Christie estate.
The makers of Doctor Who have generally avoided making pronouncements about canonicity. Showrunner Russell T Davies has explained that he does not think about the concept for the television series or its spin-offs.