Short answers, pulled from the story.
Bahlul Khan Lodi ascended the throne of the Delhi Sultanate on the 19th of April 1451 after the last Sayyid ruler Alauddin Alam Shah voluntarily abdicated. He was previously the governor of Sirhind in Punjab before establishing the fifth and final dynasty of the Delhi Sultanate.
Sikandar Khan Lodi transformed the administration of Delhi from a chaotic collection of fiefdoms into a disciplined state by compelling Pashtun nobles to submit their accounts to a state audit. He re-founded Agra as a Muslim city in 1504 and shifted the capital from Delhi to this new strategic hub.
Babur, the Timurid ruler of Kabul, defeated Ibrahim Khan Lodi at the Battle of Panipat on the 21st of April 1526. Babur led an army of 24,000 men armed with muskets and artillery against Ibrahim's force of 100,000 men and 1,000 elephants.
Mahmud Lodi declared himself Sultan after the death of Ibrahim Khan Lodi and provided around 4,000 Afghan soldiers to Rana Sanga in the Battle of Khanwa in 1527. He fled eastwards and posed a challenge to Babur two years later at the Battle of Ghaghra in 1529 before the remaining Lodi territories were absorbed into the new Mughal Empire.
Muslim subjects of the Lodis were required to pay the zakat tax for religious merit while non-Muslims were required to pay the jizya tax for receiving state protection. Hindus in some parts of the Sultanate were also required to pay an additional pilgrimage tax.