Does the time of the Adhan (call to prayer) at sunset and sunrise differ in cities like Mokattam and Katameya—which are elevated above Cairo but close to it—from Cairo's timing? And what is the extent of this difference, if any?

The time for Maghrib prayer is the sunset in the place where one resides. If the sunset times differ between the mentioned regions and Cairo, the residents of those regions are not permitted to follow Cairo's timing. Instead, they must rely on their observation of the sun or a calendar that corresponds to their local sunset. However, if the elevation mentioned does not alter the sunset time compared to Cairo, then there is no harm in adopting Cairo's timing. The key is to compare Cairo's timing with the sun's observation to determine any difference.