Short answers, pulled from the story.
Lorenzo di Pierfrancesco de' Medici entered the world on the 4th of August 1463 in Florence. His father Pierfrancesco de' Medici died when he and his brother Giovanni were still boys in 1476.
Lorenzo di Pierfrancesco studied under Marsilio Ficino, Angelo Poliziano, and Giorgio Antonio Vespucci. Vespucci was the uncle of the famous navigator Amerigo Vespucci who later became an employee of Lorenzo from 1483 onward.
In approximately 1485, Lorenzo commissioned an illuminated manuscript of Dante's Divine Comedy featuring artwork by Sandro Botticelli. The year before, in 1482, Lorenzo il Magnifico arranged his marriage to Semiramide d'Appiani which may have inspired Pallas Athene Taming a Centaur as a wedding gift.
The two brothers sided with the Republican party after returning to Florence following King Charles VIII of France invasion and ousted Piero. This shift allowed them to re-enter Florentine politics after years of exclusion and earned them the nickname Popolano meaning of the people.
By the time they reached adulthood, the brothers claimed he owed them over 100,000 ducats. Il Magnifico eventually repaid a little over half that sum in 1485.