What is the ruling on praying Fajr approximately fifteen minutes after the Adhan, given the existence of two dawns, the true and the false? And is it permissible to eat in Ramadan until 4:10 AM?

It is preferable to be cautious in the two acts of worship: prayer and fasting. Thus, a Muslim should pray after sufficient time has passed for the true dawn to rise, and abstain [from food and drink] at the time indicated by the calendar. The Fajr prayer should not be repeated after it has been performed once. If it is highly probable that the prayer was performed after the time for it had begun, then suffice with this prayer and do not repeat it.