Short answers, pulled from the story.
The Mughal Empire was conventionally founded in 1526 by Babur, who defeated Ibrahim Lodi at the First Battle of Panipat. It was formally dissolved by the British Raj after the Indian Rebellion of 1857, when the last emperor, Bahadur Shah Zafar, was deposed and exiled in 1858 to Rangoon, Burma.
Mughal is the Indo-Persian form of Mongol, but the dynasty's early followers were Chagatai Turks, not Mongols. The term was applied in India by association with the Mongols and to distinguish them from the Afghan elite who ruled the Delhi Sultanate. The Mughals themselves called their dynasty Gurkani, after their descent from Timur.
Akbar was the third Mughal emperor, reigning from 1556 to 1605, and he built the empire's highly centralised bureaucratic government. He instituted the agricultural taxes that formed the base of Mughal wealth, created the zabt land revenue system, and founded a new religion called Din-i-Ilahi while allowing freedom of religion at his court.
The Taj Mahal was built during the reign of Shah Jahan, who reigned from 1628 and ushered in the golden age of Mughal architecture. It is a UNESCO World Heritage Site described as the jewel of Muslim art in India, and it draws 7 to 8 million unique visitors a year.
Historians cite a succession of weak rulers, civil wars over succession, and the loss of revenue needed to pay the emirs and their entourages as causes of a rapid collapse between 1707 and 1720. The Sack of Delhi by Nader Shah stripped the treasury, and the empire could no longer finance the armies that had enforced its rule.
India was producing about a quarter of the world's manufacturing output up until 1750, and the Mughal economy has been described as a form of proto-industrialisation. Textile manufacturing was the largest industry, with cotton holding a 25 percent share of the global textile trade in the early 18th century, centred on the Bengal province around Dhaka.
The major Mughal emperors were Babur, who founded the empire in 1526, his son Humayun, and Akbar, who built its administration. They were followed by Jahangir, Shah Jahan, who built the Taj Mahal, and Aurangzeb, who brought the empire to its greatest territorial extent before its decline.