To what extent is the prayer timetable issued by the Sunni Endowment Office in Iraq accurate, especially regarding the timing of Fajr prayer, and is it obligatory to re-perform past prayers in the mosque if the timetable is proven to be incorrect?

It is not possible to determine the accuracy of the mentioned calendar, because it requires comparing it with the true dawn, which is not feasible. The time for Fajr begins with the emergence of the true dawn. So, whoever is able to observe the dawn and verify the calendar's accuracy, let him do so. Otherwise, let him ask the trustworthy people of knowledge in his country and act according to their fatwa. If that is not possible, then he should not pray until he is certain that the time for Fajr has begun or has a strong presumption of it.