Short answers, pulled from the story.
The first screening of Battleship Potemkin occurred on the 21st of December 1925 at a ceremonial meeting at the Bolshoi Theatre. A premiere followed in Moscow on the 18th of January 1926 at the 1st Goskinoteatre.
Sergei Eisenstein directed Battleship Potemkin after Nina Agadzhanova wrote the initial script. He abandoned an eight-episode script to focus on one episode about the battleship Potemkin involving only 41 frames from Agadzhanova's original text.
Battleship Potemkin depicts events from June 1905 when sailors aboard the ship sat anchored off the island of Tendra. The story follows a mutiny where sailors refuse maggot-infested rations and overthrow officers who inspect their sleeping quarters.
The famous Odessa Steps sequence takes place in Odessa Harbour during widespread riots sparked by the arrival of the battleship. Tsarist soldiers march down these steps firing volleys into crowds while mounted Cossacks charge fleeing people.
Battleship Potemkin faced bans in the United Kingdom until 1954 due to its revolutionary zeal. The film also experienced extended periods of restriction in France for similar reasons regarding its political content.