Short answers, pulled from the story.
The Medici Bank was founded in 1397 by Giovanni di Bicci de' Medici, born around 1360, who grew the family's wealth and made them one of the richest families in Florence. The family itself originated in the agricultural Mugello region north of Florence and is first mentioned in a document of 1230.
The House of Medici produced four popes: Pope Leo X (1513-1521), Pope Clement VII (1523-1534), Pope Pius IV (1559-1565), and Pope Leo XI (1605). They also produced two queens of France: Catherine de' Medici (1547-1559) and Marie de' Medici (1600-1610).
The Pazzi conspiracy of 1478 was an attempt by the rival Pazzi and Salviati families to depose the Medici by killing Lorenzo and his brother Giuliano during Easter services. Giuliano was killed and Lorenzo was wounded, but survived. The conspiracy involved the Archbishop of Pisa and had the tacit tolerance of Pope Sixtus IV.
The Medici were patrons of Donatello, Brunelleschi, Botticelli, Leonardo da Vinci, Michelangelo, Raphael, Machiavelli, Galileo, and Francesco Redi, among many others. Lorenzo the Magnificent served as patron to Leonardo da Vinci for seven years and invited the young Michelangelo to study the family's collection of antique sculpture.
Medici rule of the Grand Duchy of Tuscany ended with the death of Gian Gastone de' Medici on the 9th of July 1737. The grand ducal line fully extinguished on the 19th of February 1743 with the death of Anna Maria Luisa de' Medici, the Electress Palatine.
Anna Maria Luisa de' Medici signed the Patto di Famiglia on the 31st of October 1737 in collaboration with the Holy Roman Emperor and Grand Duke Francis of Lorraine. It willed all personal property of the Medici to the Tuscan state on the condition that nothing was ever removed from Florence, preserving the family's art collections in the city permanently.