Is it permissible for one who suffers from obsessive doubts to ignore a doubt concerning ablution after finishing it, and to pray with that ablution, or must she repeat it? And if she prays, is her prayer valid?

The one afflicted with Waswas (obsessive doubts) should ignore these whispers and not pay attention to their doubts. If a woman is afflicted with Waswas, she should not pay attention to doubts. So, if she doubts whether she performed ablution or not, she should act as if she did, and she is not required to repeat her prayers.