Short answers, pulled from the story.
Pope Clement VII was born Giulio di Giuliano de' Medici on the 26th of May 1478 and served as head of the Catholic Church and ruler of the Papal States from the 19th of November 1523 until his death on the 25th of September 1534. He was a member of the Medici family of Florence and is historically described as "the most unfortunate of the popes."
The Sack of Rome on the 6th of May 1527 resulted from Clement VII's shifting alliances against Holy Roman Emperor Charles V, which left him without reliable military support. Unpaid Landsknecht mercenaries, led by Charles III, Duke of Bourbon and Georg von Frundsberg, reached Rome unchallenged and sacked the city after Bourbon died in the siege. Clement was imprisoned in Castel Sant'Angelo and agreed to pay a ransom of 400,000 ducats.
Clement VII refused to annul the marriage because Catherine of Aragon was the aunt of Holy Roman Emperor Charles V, whose prisoner Clement effectively was following the Sack of Rome. Catholic teaching also held that Pope Julius II's earlier dispensation had made the marriage valid, and a validly contracted marriage could not be dissolved. The refusal ultimately led Henry VIII to break England away from the Catholic Church via the Act of Supremacy in 1534.
Clement VII commissioned Michelangelo's The Last Judgment in the Sistine Chapel, Raphael's altarpiece The Transfiguration, Michelangelo's sculptures for the Medici Chapel in Florence, Raphael's Villa Madama in Rome, and Michelangelo's Laurentian Library in Florence. As Pope he appointed Benvenuto Cellini head of the Papal Mint and arranged the contest that produced Sebastiano del Piombo's The Raising of Lazarus.
Yes. In 1533 Clement VII personally approved Nicolaus Copernicus's theory that the Earth revolves around the Sun after scholar Johann Widmanstetter explained the system to him. Clement was so pleased that he gave Widmanstetter a valuable gift in thanks. This approval came 99 years before Galileo Galilei's heresy trial.
Clement VII grew a full beard during his six-month imprisonment in Castel Sant'Angelo in 1527 as a sign of mourning for the Sack of Rome. Unlike Pope Julius II, who had previously worn a beard for nine months and then shaved it, Clement kept his beard until his death in 1534. His successor Paul III followed the example, and the fashion continued through 24 subsequent popes, down to Innocent XII, who died in 1700.