Short answers, pulled from the story.
Moghulistan was a breakaway Mongol khanate that existed from the mid-14th century until the late 17th century. It functioned as a nomadic tribal confederacy centered on the Ili River and stretching from the Tian Shan mountains to the borders of modern Kazakhstan and Kyrgyzstan.
Tughlugh Timur was the first Khan of Moghulistan who rose to power in 1347 when the Dughlat tribe appointed him to the throne. He converted to Islam in 1354 and ruled until he was expelled by Amir Husayn and Timur.
Moghulistan converted to Islam in 1354 when Khan Tughlugh Timur and 160,000 of his followers embraced the faith. This conversion marked the last instance of the Mongols converting to Islam and served as a political maneuver to justify territorial expansion.
Moghulistan ended when the Dzungar Khanate conquered the region in the early 18th century. The Yarkent Khanate was overthrown in 1705 and the Moghul kingdom of Turpan and Hami was conquered by the Zunghar Khanate shortly thereafter.
The Dughlat tribe was a powerful group that controlled extensive territories in Moghulistan and the western Tarim Basin. They administered towns in the name of the Moghul khans until 1514 and often instigated civil wars that weakened the state.
Maqsud Shah was the last of the Chagatayid house who died in 1930. His descendants had submitted to the Qing and ruled the Kumul Khanate as vassals of China until his death.