Short answers, pulled from the story.
Street Fighter Alpha Generations appeared in Japanese theaters on the 2nd of May 2009 as a bonus feature on the DVD and Blu-ray of the live-action film Street Fighter: The Legend of Chun-Li. The film was originally released by Manga Entertainment specifically for the English-language market in 2005.
The old man in Street Fighter Alpha Generations is the guardian tasked by Gouken to care for Fuka after Sayaka died in childbirth. He is the grandfather of Fuka and the former lover of Sayaka, who was Gouki's partner.
The Satsui no Hadou is a mysterious and evil life force that exists since ancient times and dwells within certain fighters. This corrupting force grows stronger as it is exploited and eventually consumes those who rely on it, turning them into inhuman monsters.
Gouki dies in the Street Fighter Alpha Generations anime film when he is killed by his master Goutetsu using the Raging Demon technique. This act of violence occurs in the distant past and serves as the catalyst for a generational curse that haunts the characters for decades.
Fuka is the granddaughter of the old man and the daughter of Sayaka, who was Gouki's lover. The old man regrets failing to prevent Fuka from following the path of Gouki, which adds emotional depth to the story of Street Fighter Alpha Generations.