Is the fixed calculation for Fajr prayer, meaning two hours before sunrise and derived using a twilight angle of 18 degrees, Islamically permissible, and which calendar should be followed, and how should the discrepancy in past times be dealt with?

The fundamental principle for knowing prayer times relies on the visible cosmic signs that the Law-Giver made indicators of the time's entry, not on calculated calendars. These calendars should not be relied upon entirely, as they are human endeavors susceptible to error and correctness. The Permanent Committee has issued a fatwa stating that these calendars should not be entrusted with prayer times; rather, reliance should be placed on the Shariah evidence.

If calendars conflict, you must do one of two things: 1. Investigate using the Shariah signs through observation. 2. If that is not possible, do not pray until you are certain that the time has entered, or you have a strong presumption of it.

As for previous prayers performed according to the calendar, if you have a strong presumption that you prayed after the time had entered, you are not required to repeat them, because a strong presumption of the time's entry is sufficient for the prayer's validity.