What is required of one who awoke late for Fajr prayer, prayed it, then discovered that the sun had risen, and does not know whether the sunrise occurred before, during, or after the prayer? Is he required to repeat it?

Your prayer is valid, and you do not need to repeat it, even if it becomes clear that the sun has risen. If you woke up and were unaware of the sunrise, and you prayed believing that the time for prayer was still open, your prayer is valid.