Does the time for the Fajr prayer end at sunrise or after the period of illumination ends? And is praying between the beginning and end of illumination cconsidered to be on time (ada') or a makeup (qada')?

The time for the Fajr prayer ends with sunrise and does not extend until the time when supererogatory prayers are no longer disliked. So, if you pray Fajr after sunrise, it is considered a missed (qada') prayer because it occurred after its prescribed time has ended. It is important to emphasize the obligation of taking measures to help one wake up for prayer, such as setting an alarm.