Short answers, pulled from the story.
Lars von Trier developed the story of Melancholia during a therapy session in 2010. The concept emerged from an observation that people suffering from depression often act more calmly than others when facing heavy pressure.
The name Justine came from the Marquis de Sade novel published in 1791 while Much of her personality was based directly on von Trier himself. The characters evolved into two maids from letters exchanged with Spanish actress Penélope Cruz who mentioned Jean Genet's play The Maids.
Poland's Platige Image company handled most of the effects seen in the opening sequence using extreme slow-motion shots of falling birds, butterflies, and a collapsing horse. Nineteen artists worked on the project for three months starting in summer 2010 to achieve this result.
Melancholia premiered at the 64th Cannes Film Festival on the 18th of May 2011 during competition screening where he made jokes about Jews and Nazis while saying he understood Adolf Hitler. The festival issued an official apology the same day clarifying he was not a Nazi or anti-Semite before declaring him persona non grata the next day.
Kirsten Dunst won the Best Actress Award at the Cannes Film Festival for her performance as Justine. Review aggregator Rotten Tomatoes showed positive reviews from critics with an average rating above eighty percent while Metacritic gave the film universal acclaim based on scores from forty different critics.