What is the ruling on one who lost her ablution due to discharge and completed the circumambulation (Tawaf) and the ritual walking (Sa'i) during Hajj, and what is the ruling on her performing the Maghrib and Isha prayers with tayammum in Muzdalifah due to the unavailability of water and the difficulty of changing clothes?

Purity is not a condition for Sa'i, unlike Tawaf. So, if the discharge stops for a period sufficient for Tawaf and ablution, then she must perform ablution before Tawaf. If it is not sufficient, then she must perform ablution, take precautions, and perform Tawaf, and what exits will not harm her because she is considered to have a continuous impurity (hadath da'im). If the discharges are from the uterus, they are pure but invalidate ablution. If they are from the bladder, they are impure, and whatever of them stains the clothes must be washed. Tayammum is not permissible if water can be obtained. She must strive to obtain water, even if it means delaying the prayer to its last time. If she is unable to find water, then Tayammum and prayer are valid. Whoever is unable to purify her garment or body, or does not find another garment, it is permissible for her to pray with her impure garment, and her prayer is valid.