The video that the Reserve Course Students see before killing themselves is based off of a real song called "Gloomy Sunday," aka "The Hungarian Suicide Song" which was composed in 1933. Surrounding the song is an urban legend which claims that the song drove many people to kill themselves during or after listening to it. The video is even called "Monokuma's Gloomy Sunday" in reference to the song's title.
For the English cast, a conscious effort was made to get most of the actors for the characters from the second game to reprise their roles. However the actors for Fuyuhiko, Peko, Akane, Ibuki and Gundham were unable to return and thus were recast for the anime.