Which Nobel Peace Prize winner, whose middle name was Gates, was vice president from 1925 to 1929?

Complete the title of Sean O'Casey's 1924 play: "___ and the Paycock". Helen Wills in 1924 and Justine Henin-Hardenne in 2004 won Olympic gold in which sport? Which dictator wrote "Mein Kampf" ("My Struggle"), first published in 1925? In 1924, Chamonix, France, hosted the first of which international sporting events? Which author created the wealthy Long Island enclave of East Egg in a 1925 novel? Self-made millionaire James Gatz reinvents himself under a new name in which 1925 novel? Which famous magician and escape artist died in 1926 following a ruptured appendix? "Red Cavalry," a famous 1926 collection of tales, was written by which Russian author?