Short answers, pulled from the story.
Areas of what would become Cairo were inhabited from pre-dynastic and early-dynastic ancient Egypt c. 6000 years ago. The city known as Fustat was founded by Amr ibn al-As in 641 or early 642 after the surrender of Alexandria.
The Abbasid Caliph al-Mutawakkil ordered a Nilometer to be built on Roda Island near Fustat in 861. This structure remains the oldest preserved Islamic-era building in Cairo today despite later repairs.
By 1340 Cairo had a population of close to half a million making it the largest city west of China. This peak occurred during the reign of the Mamluk sultan al-Nasir Muhammad between 1293 and 1341 with interregnums.
In 1906 the Heliopolis Oasis Company headed by Édouard Empain and Boghos Nubar built a suburb called Heliopolis ten kilometers from the center of Cairo. In 1905 and 1907 the northern part of Gezira island was developed into Zamalek which became an upscale neighborhood.
Between 1947 and 2006 the population of Greater Cairo went from 2,986,280 to 16,292,269. By 2009 over 63% of the population lived in informal neighborhoods that occupied only 17% of the total area.