What is the ruling regarding someone who, six months after performing ghusl following menstruation, doubts the presence of dirt in her navel during that ghusl, and what is the ruling regarding her doubt concerning the validity of wiping her head during wudu before tawaf, and is it permissible to adopt the view that purity is not a condition for the validity of tawaf out of necessity?

Dirt inside the navel, if it does not prevent water from reaching it, does not affect the validity of ghusl. If there is doubt whether it formed a barrier that existed before or after ghusl, the default is that it appeared afterwards, and the ghusl is valid. Doubt about the manner of wiping the head does not invalidate wudu', as the default is its validity until proven otherwise. The questioner is advised to avoid obsessive thoughts, as their harm is immense, and their cure is to disregard them.