Will I be sinful if I ignore the obsessive whispers of swearing to repeat the prayer or ablution? And does water entering the throat during rinsing in the mouth in Ramadan invalidate the fast? And what is the ruling on doubting purity after ghusl from menstruation?

There is no cure for obsessive whispers (waswas) except to disregard and ignore them. If you succumb to them, it will lead to great evil. If an oath or a breach of an oath occurs under the influence of obsessive whispers, it holds no validity. Regarding water that you doubt reached the throat, the default is that it did not. Even if some of it did reach the throat, it does not invalidate the fast as long as you did not intentionally swallow it. What you did by performing ghusl after the cessation of menstruation is correct and obligatory.