Short answers, pulled from the story.
The Turco-Mongol tradition was an ethnocultural synthesis that arose in Asia during the 13th and 14th centuries among the ruling elites of the Golden Horde and the Chagatai Khanate. Mongol ruling elites gradually adopted Turkic languages and Islam while retaining Mongol political and legal institutions, producing a distinct identity known as Turco-Mongol.
The Turco-Mongols founded the Kazakh Khanate, the Crimean Khanate, the Astrakhan Khanate, the Khanate of Kazan, the Timurid Empire, and the Mughal Empire, among others. Babur, born in 1483 and a descendant of Timur, established the Mughal Empire, which ruled much of the Indian subcontinent.
Uzbeg Khan assumed the throne of the Golden Horde in 1313 and declared Islam the state religion. By 1315 he had successfully Islamicized the Horde, enforcing the conversion by executing Jochid princes and Buddhist lamas who opposed his religious policy.
The Mongol elites of the Chagatai Khanate adopted the Chagatai language, a descendant of Karluk Turkic. Chagatai was the native language of the Timurid dynasty and is the direct predecessor of modern Uzbek and Uyghur.
Turco-Mongol elites of Karluk ethnicity became patrons of the Turco-Persian tradition and carried it outward through conquest. It became the dominant culture of the ruling classes across North India, Central Asia, the Tarim Basin in northwest China, and large parts of the Middle East, spread through states such as the Timurid Empire and the Mughal Empire.
According to John Joseph Saunders, Timur was "the product of an Islamized and Iranized society" and not a steppe nomad in the traditional sense. Timur called himself the "Sword of Islam," patronized religious and educational institutions, and defeated the Knights Hospitaller at the Siege of Smyrna.