Short answers, pulled from the story.
Napoleon and his army entered Moscow on the 14th of September 1812. The city fell without a fight after Field Marshal Mikhail Kutuzov ordered a retreat from Borodino eastwards to preserve the Russian army.
Arson occurred around the city when the French entered on the 14th of September 1812, and strong winds fanned flames across the city until the 18th of September. The fire destroyed most of Moscow and was reportedly visible over 215 km away.
The French abandoned the city voluntarily on the night of the 19th of October 1812 because they were short on supplies and saw the fall of the first snows. Napoleon intended to attack and defeat the Russian army but could not break out into unforaged country for provisions.
A police survey from the beginning of 1812 found that the city hosted 270,184 residents. In addition to them, around 10,000 to 15,000 wounded and sick Russian soldiers also remained within the city limits.
Only Marshal Édouard Mortier's corps remained in Moscow as the city's Governor General when Napoleon departed on the 19th of October 1812. Napoleon ordered Mortier to destroy Moscow and then rejoin the main army.