Short answers, pulled from the story.
Christmas in Russia is celebrated on the 7th of January on the Gregorian calendar, which corresponds to the 25th of December on the Julian calendar used by the Russian Orthodox Church. The 13-day difference from Western Christmas dates stems from this calendar distinction.
A decree of the Stalinist regime abolished all religious holidays, including Christmas, in 1929. The Bolsheviks had argued that Christmas was a pagan sun-worshipping ritual and dismissed the Christmas tree as a bourgeois German import. The holiday remained officially suppressed for most of the 20th century.
Ded Moroz is the traditional Russian gift-bringer, described as the counterpart of Saint Nicholas or Father Christmas but a little taller and less stout. Rooted in Slavic folklore, he travels with his granddaughter Snegurochka on a sleigh pulled by a trio of horses.
In 1935, the Soviet state revived many Christmas traditions as secular New Year's celebrations. The Christmas tree was renamed the New Year's fir tree, and traditions including Ded Moroz's visits and gift-giving were reassigned to January 1st, stripping them of religious meaning.
Christmas was reinstated in 1991 following the dissolution of the Soviet Union. In 1992, it became a national public holiday, falling within the ten-day holiday period at the start of the new year.
The traditional Christmas Eve dinner, called the Holy Supper, consists of 12 dishes honoring each of the Twelve Apostles. No meat is served because Christmas Eve is a mandatory fasting day in the Russian Orthodox tradition.