Judgement at Nuremberg
No, you can win an Oscar for directing a short film, but you can't win an Oscar for starring in a short film.
Chicago
Wings (1927)
The Accused
Technically, it was Flowers and Trees (1932). It was the first film to win the Oscar for Best Animated Short. Snow White and the Seven Dwarfs did not win and Oscar but it did receive a special honorary Oscar for its achievement as the first full-length animated film in history. The first feature length animated Disney film to win a competitive Oscar was Pinnochio. It won Best Score and Best Song (When You Wish Upon A Star). Ironically, as of 03/07/2010, Disney has yet to win the Oscar for Best Animated Feature (unless you count Pixar as part of Disney).
No, "Tsotsi" is not the first African movie to win an Oscar. It won the Academy Award for Best Foreign Language Film in 2006, but the first African film to receive an Oscar was "Yesterday," a South African film that was nominated in 2005. Additionally, the film "The Gods Must Be Crazy" was nominated in 1981, although it did not win.
No. But it was nominated for an Oscar in the Best Foreign Language Film category.
No, Lagaan was the first Indian (Hindi language) film nominated for Best Foreign Language Film, but it did not win.
No. The entry from Belgium was nominated for Best Foreign Language Film. But the Oscar went to "A Separation" from Iran.
The Miracle Worker
Wall-e
Yes, it did.