Short answers, pulled from the story.
Ferdinand Karl, Archduke of Austria-Este, was the son of Holy Roman Emperor Franz I and Maria Theresa of Austria, born on the 1st of June 1754 at Schönbrunn Palace in Vienna. He served as Governor of the Duchy of Milan from 1771 to 1796 and founded the House of Austria-Este through his marriage to Maria Beatrice Ricciarda d'Este.
The Napoleonic Wars prevented Ferdinand Karl from ever reigning over Modena. Napoleon's invasion of Milan in 1796 forced Ferdinand and his family to flee, and Modena itself overthrew its monarchy to join the Cisalpine Republic. Ferdinand held only the title of titular Duke of Modena and Reggio after 1803, without actual rule.
Two operas were performed at the festivities for Ferdinand Karl's marriage on the 15th of October 1771: Ascanio in Alba by Mozart and Il Ruggiero by Johann Adolph Hasse.
The Treaty of Campo Formio of 1797 granted Ferdinand Karl's father-in-law, Duke Ercole III, the Duchy of Breisgau in southwest Germany as compensation after Napoleon's forces seized Modena. When Ercole III died in 1803, Ferdinand inherited Breisgau, though he later ceded it to the Grand Duchy of Baden under the Treaty of Pressburg in 1805.
Ferdinand Karl and Maria Beatrice d'Este had ten children. Three died in infancy or early childhood. Notable survivors include Francis IV, who became Duke of Modena; Ferdinand Karl Joseph, who commanded the Austrian army during the Napoleonic Wars; and Maria Ludovika, who married Emperor Francis I of Austria.
Ferdinand Karl died in Vienna on the 24th of December 1806 and is buried in the Imperial Crypt in Vienna.