Short answers, pulled from the story.
Joseph L. Mankiewicz was the first. He won for A Letter to Three Wives in 1949 and then for All About Eve in 1950, the first back-to-back wins in the category's history.
Sarah Y. Mason was the first woman to win specifically for an adaptation. She took the award in 1932-33 for Little Women, adapting Louisa May Alcott's novel, sharing the prize with her husband Victor Heerman. Frances Marion had previously won a unified screenplay award in 1929-30, before the Academy separated original and adapted categories.
James Ivory is the oldest winner at 89 years and 270 days. He received the award for Call Me by Your Name.
Michael Wilson was blacklisted when he earned his second win, for The Bridge on the River Kwai. The Academy presented the award to Pierre Boulle, the novel's author, as a front. The Academy later officially recognized Wilson as the true winner.
Three sibling pairs have won. Philip G. Epstein and Julius J. Epstein won together for Casablanca in 1943; James Goldman won for The Lion in Winter while his brother William Goldman won for All the President's Men; and Joel Coen and Ethan Coen won for No Country for Old Men.
Geoffrey S. Fletcher was the first, winning for Precious in 2009. He was also the first African American to win any Oscar in the writing categories.