To what extent is the statement valid that there is an error in determining prayer times, especially Fajr prayer, and that Muslims pray Fajr before its due time, along with mentioning the hadiths related to the false dawn (al-fajr al-kadhib) and the redness in the sky?

The statement that Muslims pray Fajr before its time is not entirely accurate, for there are two types of Fajr: the false dawn (Fajr Kadhib) and the true dawn (Fajr Sadiq). The false dawn appears as an elongated, vertical light, like a wolf's tail, and then disappears. As for the true dawn, it spreads horizontally across the horizon, and its light continuously increases until the sun rises.

The primary basis for determining prayer times are the Shar'i (legal) signs. There is no harm in relying on prayer time calendars approved by trustworthy scholars, as long as they do not contradict the Shar'i signs. However, unknown calendars should not be fully relied upon.