The history of Egypt started to diverge from OTL in 1236 when the Choresmians took Baghdad, toppled and imprisoned the old Abbasid caliph Al-Mustansir. Some of his relatives fled to Egypt and the Rum-Seljuks, helping those lands with claims for the Caliph title.
Still some things happened as OTL: 1244, Jerusalem was conquered by sultan as-Salih. (This was expectable, since the city lacked the hinterland for a better defense.) The only difference to OTL was that he used Mamluk soldiers for the attack instead of hired Choresmians. The city was damaged less than IOTL. 1248-54, the Europeans made the Sixth Crusade against Egypt, which stayed without success.
1250 (still as OTL), the Mamluks under Aybak took power in Egypt. At the moment, he had to share power with the widow of the last Ayyubid sultan, Shajar ad-Durr. 1257 Shajar ad-Durr was murdered after she had Aybak murdered; Qutuz became new sultan of Egypt. 1260, OTL Baibars I did not become ruler of Egypt, since he still lived in the Kipchak lands - he wasn't enslaved by Mongols. However, the Mamluks attacked the Crusader States, conquered Gaza, Askalon and Jaffa - earlier than OTL.
1290, Aragon and Egypt made an alliance - the first important alliance between a Christian and a Muslim state.
War with Choresm
1334, Choresm and Mamluk Egypt clashed over Syria / Palestine. Choresm won and annexed northern Palestine, but news about unrests in Afghanistan forced the Shah to cancel further advancing.
Egypt wanted revenge and allied in 1352 with the Sultanate of Konya against Choresm. The invaded Syria together, defeated the Choresmian armies several times. 1357, Choresm was in a desperate situation, but now the Shah hired the Assassins to get rid of his enemies. The general of the Mamluks and the Sultan of Konya were killed. Choresm made peace, only gave northern Palestine back to Egypt.
1387-89, Egypt was hit by the Black Death.
Egypt under the Seljuks
In 1429, the new Circass dynasty had come to power in Egypt; but after a short war 1450/51 with the Rum-Seljuks, where they demonstrated their military power (cannons, large standing army), the Seljuks made Egypt their tributary. Now Persia and Choresm were the only other major Muslim powers left.
A Chinese treasure fleet sailed up the Red Sea and sent a delegation to Egypt 1452-56 (3149, Yang Water Monkey / 3153, Yang Fire Rat in their calendar). On their return, they also spread tales about the Christian countries.
Since 1650 however, being separated from the rest of the Seljuk empire, the governors of Egypt started to aim for more independence.
1725-32, Egypt rose against the Seljuk rule. Finally, sultan Kilij Arslan VI gave in and allowed Egypt to transform into an allied, tribute-paying but otherwise independent sultanate.
During the Seljuk Wars, the Sinai became the target of France. After the Great Seljuk War and the fourth French-Seljuk War, it was occupied by France; but after the anti-French War and the beginning of the French Republican Wars, it was occupied by the Seljuks again.