First theatre to ever show a true double-feature, that is to say, two feature films: The Glaciarium down under (Australia that is). The two films were The Lost Chord from 1911 and The Fall of Troy from 1910. The first is an Australian movie the second is an Italian job. The date of the double feature - May 15, 1911. In case you're wondering about the name, Glaciarium, it's mainstay was putting on ice skating shows. There were five Glaciariums in Australia, two in Sydney alone. The double feature ran at the Melbourne one. But this spectacular ice show is from one of the Sydney Glaciarium (ah, for a Glaciarium in my hometown)
The first successful two color process: Kinemacolor, developed by George Smith. When? 1906. He made a short film (they were all short in 1906) of his son and daughter in colorful clothes playing in the yard. And of course, they're waving a Union Jack.
The first double exposure: Who else? Georges Melies. It came in 1898's Cave of the Demons.
The first time two characters played by the same actor physically interacted: Hang on, because it's a lot earlier than you think - 1921. Mary Pickford played Little Lord Fauntleroy and his mother. Here's the shot:
That's Mary Pickford shaking the hand of Mary Pickford. One scene where she, as Little Lord Fauntleroy, kisses herself, as the mother, on the cheek took over 15 hours to shoot.
First, and only time, an actor was nominated twice in the same year for the same performance: 1944's Going My Way featured Barry Fitzgerald in a supporting role but the Academy nominated him for Best Actor and Best Supporting Actor. He won the supporting Oscar and the Academy immediately changed the rules: When an actor receives votes for nomination in two different categories whichever he or she gets the most in is the category for which they are nominated.
First time two different actors both won Oscars for playing the same character: March 1975, when Robert DeNiro took home the Best Supporting Actor Oscar for playing Vito Corleone in the 1974 film The Godfather, Part II, the same character Marlon Brando had played in the 1972 film The Godfather, also winning an Oscar for his portrayal.