Short answers, pulled from the story.
Uzbeg Khan declared Islam the state religion of the Golden Horde in the year 1313. This decision involved the execution of Buddhist lamas and Jochid princes who resisted the change. The shift marked a cultural revolution that transformed Mongol conquerors into Turco-Mongols.
Mongol elites in the Golden Horde adopted the Kipchak language, which became the lingua franca of the region. In the Chagatai Khanate, the Mongols adopted the Chagatai language, a descendant of Karluk Turkic. By the 18th century, Mongolian had disappeared from these conquered lands and was replaced entirely by the Tatar language.
Timur was born in 1336 and founded the Timurid Empire in Central Asia. He styled himself the Sword of Islam and converted nearly all Borjigin leaders to Islam during his lifetime. His capital of Samarkand became a center of a large Muslim Sultanate.
Babur founded the Mughal Empire in 1526 and was born in 1483. He died in 1530 and brought the traditions of the Chagatai Khanate to the Indian subcontinent. The Mughal Empire became the culmination of the Turco-Mongol tradition in South Asia.
Uzbeg Khan married a princess from his family to Al-Nasir Muhammad, the Sultan of Egypt. This alliance created a bond between the Golden Horde and the Mamluk Sultanate in Cairo. The connection helped solidify the Turco-Mongol tradition through shared religious and cultural identity.