Short answers, pulled from the story.
The Yuan dynasty was formally founded in 1271 by Kublai Khan, the fifth khagan-emperor of the Mongol Empire from the Borjigin clan. Kublai proclaimed the dynasty in the traditional Han style and named it the Great Yuan, though the conquest of southern China was not complete until 1279.
The Yuan dynasty divided its population into four ranked groups: Mongols at the top, followed by the Semu (non-Mongol foreigners from the west and Central Asia), then the Han (former subjects of the Jin dynasty in northern China), and finally the Nan or Southerners (former subjects of the Southern Song dynasty). The ranking was based primarily on the order of submission to Mongol rule, not solely on ethnicity.
The Yuan dynasty collapsed following widespread famine and rebellion from the late 1340s onward. The Red Turban Rebellion, which began in 1351, grew into a nationwide uprising. In 1368 the last Yuan emperor Toghon Temur fled north to Shangdu as forces of the newly founded Ming dynasty, led by Zhu Yuanzhang, approached Khanbaliq. Yuan remnants retreated to Mongolia and continued as the Northern Yuan until 1635.
The Yuan period saw the development of Chinese drama and the novel, the spread of blue and white porcelain beginning in the kilns of Jingdezhen in the early 14th century, and major advances in mathematics and astronomy. Annual sales of printed calendars and almanacs reached over three million by 1328. The period also saw the introduction of crops including carrots, cotton, and sorghum, and the transmission of Chinese printing and medical techniques westward.
Marco Polo was a Venetian merchant who visited the Yuan court and wrote the most influential European account of Yuan China. His book, known in English as the Travels of Marco Polo, appeared around 1299 and described life in the Yuan capital, which he called Cambaluc. His account later helped inspire Christopher Columbus to seek a passage to the Far East.
The Yuan dynasty tolerated multiple religions including Buddhism, Islam, Christianity, and Manichaeism. Kublai Khan favored Tibetan Buddhism, particularly the Sakya sect, which became the de facto state religion. Before the end of the dynasty, 14 leaders of the Sakya sect had held the post of Imperial Preceptor. The Mongols also restricted Islamic practices such as halal slaughter and circumcision, which contributed to Muslim discontent and eventually to Muslim participation in anti-Yuan rebellions.