Short answers, pulled from the story.
Mehmed II, born on the 30th of March 1432 in Edirne, was sultan of the Ottoman Empire twice, from August 1444 to September 1446 and from February 1451 to May 1481. He is commonly known as Mehmed the Conqueror, or Fâtih Sultan Mehmed, and was the son of Sultan Murad II and a slave mother named Hüma Hatun.
Mehmed II conquered Constantinople on the 29th of May 1453, at the age of twenty-one, after a fifty-seven-day siege. The conquest brought an end to the Byzantine Empire, and he moved the Ottoman capital from Adrianople to the city.
Mehmed II claimed the title caesar of Rome, or Qayser-i Rûm, because Constantinople had been the capital of the Roman Empire since Constantine I consecrated it in 330 AD, and he argued that whoever held that capital ruled the empire. The Eastern Orthodox Church recognized the claim, but the Catholic Church and most of Western Europe rejected it.
Mehmed II conquered Constantinople in 1453, the Despotate of the Morea in 1458 and 1460, the Empire of Trebizond in 1461, Serbia by 1459, Bosnia in 1463, and Albania by 1478. His forces also captured Otranto in Italy in 1480.
Mehmed II gathered Italian artists, humanists, and Greek scholars at his court, called Gentile Bellini from Venice to paint his portrait, and built a library of over eight thousand manuscripts in Persian, Ottoman Turkish, Arabic, Latin, and Greek. He also built the Fatih Mosque and eight madrasas, and patronized Kritiboulos of Imbros, who wrote a Greek History of Mehmed the Conqueror.
Mehmed II died on the 3rd of May 1481. After his death, quarrels about his succession possibly prevented the Ottomans from reinforcing their garrison at Otranto in Italy, which was retaken by Papal forces that year. He is considered a hero in modern-day Turkey, with Istanbul's Fatih district, the Fatih Sultan Mehmet Bridge, and the Fatih Mosque named after him.