Singin in the Rain
An American in Paris
IMHO, The Conversation was his best acting performance. At least amongst the 25 films I've seen where he makes an appearance.
Blazing Saddles, Young Frankenstein, or Silver Streak, depending on your tastes.
Gene Kelly: Anatomy of a Dancer, the documentary on the life and death of Gene Kelly
Not too sure but there is a whole list of movie acted in, movies directed, and soundtracks. Just go to IMDb just search his name
The second one