Is it necessary to repeat the Witr prayer, the two Sunnah Rak'ahs before Fajr (Sunnat al-Fajr), the Fajr prayer, or the Duha prayer, if the ritual purification (Wudu') was performed with the intention for the two Sunnah Rak'ahs before Fajr, and then the person prayed Witr, then the two Sunnah Rak'ahs before Fajr, then Fajr, and then Duha?

If you perform ablution (wudu') with the intention of the two rak'ahs of the Fajr supererogatory prayer (Sunnat al-Fajr), you are permitted to pray with this ablution as many obligatory (fara'id) and supererogatory (nawafil) prayers as you wish. This is because removing ritual impurity for a supererogatory prayer is the same as for an obligatory prayer. When ritual impurity is removed, the purification becomes valid. Therefore, the Witr prayer, the Fajr supererogatory prayer, the Fajr obligatory prayer, and the Duha prayer are all valid with your ablution, and you do not need to repeat them.