Short answers, pulled from the story.
Mamluk means "one who is owned," or slave. The Mamluks were non-Arab, ethnically diverse enslaved mercenaries and slave-soldiers, mostly of Turkic, Caucasian, Mongol, and Eastern and Southeastern European origin, who were purchased, converted to Islam, trained, and then freed to serve in high-ranking military and administrative roles in the Muslim world.
The massive slave military class developed in the 9th-century Abbasid Caliphate based in Baghdad, under the caliph al-Muʿtaṣim. Historians distinguish the earlier Ghilman system at Samarra from the Mamluk system, which added systematic training of young slaves after the caliphate returned to Baghdad in the 870s.
The Mamluk Sultanate centered on Egypt and Syria existed from 1250 to 1517. It was founded after the viceregent Qutuz took power, and it ended when the Ottoman sultan Selim I captured Cairo on the 20th of January 1517.
At the Battle of Ain Jalut in 1260, the Mamluk army led by Qutuz drew a reduced Ilkhanate force of about 18,000 men, left under the Christian lieutenant Kitbuqa, into an ambush near the Orontes River. The Mamluks routed them and captured and executed Kitbuqa.
Mamluks were bought as children without families and raised in barracks to view the sultan as their father and other Mamluks as their brothers. A freeborn soldier had a biological family commanding his first loyalty, while a Mamluk's loyalty ran to the household that raised him.
On the 1st of March 1811, Muhammad Ali invited leading Mamluks to his palace and had his forces kill almost all of the 600 to 700 who paraded, near the Al-Azab gates, in what became known as the Massacre of the Citadel. An estimated 3,000 Mamluks and relatives were killed across Egypt the following week.
Yes. Mamluks held power in several regions, including the Mamluk Sultanate in Delhi founded by Qutb al-Din Aibak in 1206, which lasted until 1290, and in Iraq, where Mamluk officers of Georgian origin ruled from 1747 to 1831 until the Ottomans overthrew Dawud Pasha.