Short answers, pulled from the story.
Mu'iz-ud-din Umar Shaikh Mirza entered the world in 1356 as a son of Timur, the founder of the Timurid dynasty. His mother was Tolun Agha, who held the status of a concubine within the royal household.
Umar Shaikh proved himself an accomplished warrior and skilled horseman during his early years. He defeated Qamar-ud-din Dughlat quickly and forced Tokhtamysh to flee from Timur's advancing forces multiple times between 1388 and 1391.
In 1394, Umar Shaikh died after being shot in the neck by an arrow. The projectile came from the Tuz Khurmatu fortress located near Baghdad while he answered a summons from his father at the time of his death.
Timur appointed him governor of Fergana in 1376 and later bestowed the former territory of Fars upon Umar Shaikh for administration in 1393. The prince had previously governed Ferghana but now received this new province.