Short answers, pulled from the story.
Baybars was born in the steppe region north of the Black Sea known as Dasht-i Kipchak. His birth year remains a subject of historical debate with some sources placing it around 1223 and others suggesting late 1227 or early 1228.
Baybars succeeded Qutuz as Sultan of Egypt following the assassination of Qutuz during a hunting expedition after the Battle of Ain Jalut in 1260. He immediately marched on Damascus to crush resistance from Alam al-Din Sinjar al-Halabi and secured the city by the 17th of January 1261.
Baybars commanded the vanguard of the Mamluk army at the Battle of Ain Jalut in 1260 against the Mongol Ilkhanate. His forces inflicted the first substantial defeat upon the Mongol army which marked a turning point in history and secured Egypt and Syria against further Mongol expansion for decades.
Baybars besieged Antioch in 1268 because Christians had aided the Mongols and he engaged in a lifelong struggle against Crusader kingdoms. He captured the city on May 18 despite promising to spare inhabitants then broke his promise to raze the city and kill or enslave much of the population.
Baybars responded to the destruction of Aswan by sending a well-equipped army from Cairo in early 1276 to defeat the Nubians in three battles at Gebel Adda Meinarti and Dongola. King David fled upstream into al-Abwab before being handed over by its ruler so Baybars executed David and completed the conquest of Medieval lower Nubia ruled by Banu Kanz.