Short answers, pulled from the story.
Roman Egypt began in August 30 BC following the Battle of Alexandria when Octavian seized the territory as his personal possession. The legal status became an imperial province in January 27 BC after Octavian received the honorific name Augustus.
A prefect of Aegyptus held combined responsibility for military security, finance, taxation, and justice throughout the period. This governor was appointed by the emperor with equestrian rank rather than senatorial status and earned an annual salary of 200,000 sesterces.
Romans established a social hierarchy revolving around ethnicity and place of residence where Greek citizens held the highest status and rural Egyptians occupied the lowest class. Native Egyptians paid three times more per aroura of land in tax rates than elites and four to five times more than Alexandrians while being barred from serving in legions.
Around 8,000 soldiers resided within Alexandria's huge population during the 2nd and 3rd centuries. At least one legion remained permanently stationed at Nicopolis alongside strong cavalry forces that guarded the prefect's residence against uprisings.
Volume trade internal and external reached its peak during the 1st and 2nd centuries when Aegyptus shipped massive amounts of grain downriver north to feed the population of Alexandria. These shipments served as a critical lifeline for Rome throughout the empire despite later economic problems evident by the end of the 3rd century.