Short answers, pulled from the story.
The Timurid Empire was founded by Timur, also known as Tamerlane, a warlord from the Barlas tribe, a Mongol group that had become Turkicized in Central Asia. He established the empire in 1370 and ruled it until his death in 1405.
At its height, the Timurid Empire dominated Greater Iran and comprised modern-day Iran, Iraq, Afghanistan, much of Central Asia, the South Caucasus, and parts of contemporary Pakistan, North India, and Turkey.
Persian was the official state language of the Timurid Empire, serving as the language of administration, history, poetry, and the law. Chaghatay Turkic was the native home language of the Timurid family, while Arabic held the place of science, theology, and philosophy.
The Timurid Empire declined rapidly during the second half of the fifteenth century due to succession disputes and civil wars. Persia fell to the Safavid Empire under Shah Ismail I, while the Uzbeks under Muhammad Shaybani conquered Samarkand and Herat in 1505 and 1507 and founded the Khanate of Bukhara.
The Mughal Empire was founded in 1526 by Babur, a Timurid prince and son of the governor of Fergana, Umar Shaikh Mirza II. Though commonly called Mughal, the dynasty was directly inherited from the Timurids. The Mughal dynasty's nominal rule ended when the British Empire abolished it following the 1857 rebellion.
The main symbol of the Timurids was the sign of Timur: three equal circles arranged in the form of an equilateral triangle. Timur ordered this device placed on his seal, stamped on coins, and carved into buildings. The Castilian ambassador Ruy de Clavijo, who died in 1412, described it as signifying that Timur was lord of all three quarters of the world.