Is the 'Umrah of someone suffering from Waswasah (obsessive-compulsive disorder) valid, given her repeated Wudu' (ablution) and her doubt concerning the intention for Sa'y (the ritual walking between Safa and Marwah) and Tawaf (circumambulation of the Kaaba)? And is it permissible for her to adopt the view that purity is not a condition for Tawaf?

Your 'Umrah is valid, Allah willing. Disregard the obsessive doubts concerning the intention. Do not pay attention to what Satan suggests to you, that you did not make an intention, for the intention for Sa'i is not obligatory according to many scholars. As for purity for Tawaf, you may adopt the view of those who do not consider it obligatory. One who suffers from obsessive doubts is permitted to avail themselves of the easiest opinions. If you performed ablution, do not pay attention to doubts about its invalidation. Hold fast to the principle that your purity remains until you achieve absolute certainty of its invalidation.