Short answers, pulled from the story.
Qachuli founded the Barlas clan within the Khamag Mongol confederation in Northern Mongolia. He was the twin brother of Qabul Khan, the first ruler of the Khamag Mongol Confederation, and is recorded as either the son of Tumanay Setsen or of Tumbinai Khan, chief of the Borjigin.
The Barlas produced two major imperial dynasties: the Timurid Empire, founded by Timur in the 14th century and covering Central Asia, Persia, the Caucasus, Afghanistan, and parts of Anatolia and Mesopotamia; and the Mughal Empire in the Indian subcontinent, founded by Babur, a descendant of Timur.
Originally Mongol speakers, the Barlas adopted Chagatai, a Turkic language of the Qarluq branch that was heavily influenced by Arabic and Persian. This shift occurred as a result of extensive contact with the native populations of Central Asia after the tribe settled in Transoxiana.
The Barlas converted to Islam after settling in Central Asia, abandoning the Tengrism practiced by their Mongol ancestors. The conversion was driven by extensive contact with the native population of the region.
The Barlas controlled the region of Kish, known today as Shahrisabz in present-day Uzbekistan. All lineages of the tribe appear to have been associated with this region, and unlike most neighboring tribes, the Barlas were sedentary rather than nomadic.
According to the historian Rashid al-Din Hamadani, the Barlas and the imperial Mongol ruling clan of Genghis Khan shared a common ancestor in Tumbinai Khan. Qarachar Barlas, great-grandson of the tribe's founder Qachuli, served as a minister and military commander under Genghis Khan and was later made governor of Transoxiana under Chagatai Khan.