Is the fast of one who drank water out of thirst six minutes after the Fajr adhan valid, and what is the interpretation of seeing a room light up and dim when returning to sleep?

The decisive factor is the emergence of true dawn (Al-Fajr Al-Sadiq), based on the Almighty's saying: "And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]." If the muezzin ascertains the true dawn, then it is not permissible to eat and drink after his adhan, and the questioner must make up for the fast if he intentionally drank, or if he relied on an accurate calendar. However, if the muezzin calls the adhan preemptively, then there is no harm in drinking until dawn appears, while emphasizing that it is not permissible for the muezzin to intentionally call the adhan before its time.