Short answers, pulled from the story.
Bairam Khan was a military commander and statesman who served as regent and commander-in-chief under the Mughal emperors Humayun and Akbar. He was the guardian and chief mentor of Akbar, played a decisive role in restoring Mughal authority in India after Humayun's exile, and was honoured with the title Khan-i-Khanan, meaning "King of Kings".
Bairam Khan commanded the Mughal army at the Second Battle of Panipat on the 5th of November 1556 against Hemu, the Vakil of Adil Shah Suri. The Mughals won the fiercely contested battle, Hemu was captured and killed, and Delhi and Agra were subsequently reconquered for the empire.
When Humayun died on the 27th of January 1556, Bairam Khan concealed the emperor's death from the public. He arranged for a loyal cleric named Mullah Bekasi, who resembled Humayun, to appear in imperial robes from the fort balcony each day until Akbar could be crowned on the 14th of February 1556.
Akbar removed Bairam Khan from power in March or April 1560 after a series of conflicts, including Bairam Khan making decisions unilaterally, restricting Akbar's personal spending, and having two of Akbar's personal mahouts executed over incidents involving elephants. Akbar offered him retirement, a land grant, or the hajj pilgrimage to Mecca.
Bairam Khan was assassinated on the 31st of January 1561 at Sahasralinga Tank near Anhilwad Patan in Gujarat. He was stabbed by Mubarak Khan Lohani, whose father had died fighting the Mughals at the Battle of Machhiwara in 1555; a second attacker struck him on the head, and Bairam Khan died repeating the takbir.
Abdul Rahim Khan-i-Khanan was the son of Bairam Khan. After his father's assassination, he was brought to Akbar's court at Agra and went on to become one of the nav-ratans, the nine gems, of Akbar's court, inheriting his father's honorific title of Khan-i-Khanan.