Short answers, pulled from the story.
Cardinal Alessandro Farnese (1520-1589) was an Italian cardinal, diplomat, and major patron of the arts who was the grandson of Pope Paul III. He is significant for his role in multiple papal elections, his decades of diplomatic service between the French crown and the Holy Roman Empire, and for assembling the greatest private collection of Roman sculpture since Antiquity, now largely held in Naples.
Alessandro Farnese was fourteen years old when his grandfather Pope Paul III appointed him Cardinal Deacon of Sant'Angelo in Pescheria on the 18th of December 1534, just two months after Paul III's own election to the papacy.
After Alessandro Farnese's death in 1589, his collection of Roman sculpture passed by inheritance to the Bourbon-Parma kings and is now mostly held in Naples. He also commissioned the Farnese Hours, completed in 1546 after nine years in the making, which is now the property of the Morgan Library in New York.
Alessandro Farnese funded the building of the Church of the Gesù in Rome, designed by Giacomo Vignola and Giacomo della Porta between 1568 and 1575. He is buried before the high altar in the Gesù; forty-two cardinals participated in his funeral ceremonies.
Farnese acquired a northern portion of the Palatine Hill in 1550 and converted ruins from the palace of the Emperor Tiberius into formal gardens that became one of the first botanical gardens in Europe. The plant Acacia farnesiana and the biochemical farnesol both derive their names from these gardens.
Farnese was blocked from election in 1572 when King Philip II of Spain sent explicit word, delivered by Cardinal Granvelle on the night the conclave opened, that Farnese should not attempt to become pope. In 1566 he could muster between twenty-eight and thirty votes but needed thirty-five, and in 1555 he declined the Imperial faction's offer of support because he lacked endorsement from either the Emperor or the King of France.