Is the prayer valid, and must it be repeated, if the questioner suffers from waswas (obsessive doubts) and believes that something was emitted during the prayer, and doubts having completed the recitation of the surahs, even though she completed the prayer and did not repeat it?

The cure for obsessive thoughts is to ignore and disregard them. If Satan instigates an obsessive thought about something having exited, then one should rely on the default assumption, which is the persistence of purity. Its invalidation should only be declared with absolute certainty. When reciting Al-Fatiha or anything else, it suffices to recite it once and not repeat it. The prayer is valid, and the obsessive thought does not harm it. There is no need to inspect or verify if something has exited; rather, one should act based on the default assumption, which is that nothing has exited.