How can one get rid of the obsessive doubts (waswas) concerning intention and ritual purity (tahara), and what is the ruling on the fast of someone afflicted by these obsessive doubts, and is their fast valid?

The fasting of a woman with vaginal discharge is valid because ritual bathing (ghusl) from janabah (major ritual impurity) is not a condition for the validity of fasting. As for the discharges themselves, they do not necessitate ghusl unless the woman is certain that the discharge is semen (maniyy). If she is unsure whether it is semen, madhiy (pre-seminal fluid), or other vaginal secretions, ghusl is not obligatory for her. Rather, she has the choice and can assign to this discharge the ruling of whichever of these secretions she wishes.