Is the obligatory Fajr prayer valid if performed before its Sunnah, and must it be repeated?

Your prayer is valid and does not need to be repeated. Deliberately performing the Sunnah (definition) of Fajr after the Fajr obligatory prayer does not invalidate either of them. The general rule is that the Sunnah of Fajr should be prayed first, unless there is not enough time to perform the obligatory prayer, in which case the obligatory prayer should be prioritized. If the Sunnah of Fajr were prayed before the obligatory prayer in such a situation, it would not be valid. If the obligatory Fajr prayer is performed at the very end of its time, do not perform the Sunnah immediately afterward; rather, wait until the sun rises and is elevated, in order to avoid the prohibited time for prayer. We advise you to maintain congregational prayer in the mosque due to its immense rewards.