Does the wetness a woman felt during Tawaf, of which she found no trace afterward, affect the validity of her Umrah? And does the persistent wetness a woman experiences before and after her menstrual cycle invalidate Wudu and other acts of worship?

Your 'umrah (definition) is valid, as doubt about something exiting during tawaf (definition) does not invalidate the certainty of purity, especially since you did not find anything after the tawaf. Vaginal discharge, according to the preponderant opinion, invalidates ablution (wudu'), but some jurists hold that it does not invalidate ablution if it is continuous. Ibn 'Uthaymeen said: "It is pure, and ablution is not required for it if a person performs ablution for the first time after an impurity, and he remains in a state of purity." Discharge related to menstruation may or may not be menstruation.