Is fasting on the 10th of Ramadan valid, and what should be done regarding the prayers and days the questioner fasted without fully washing her hair and head from menstruation?

Your fast is valid, and you are not required to make up for it, as ghusl from menstruation or janabah is not a condition for the validity of the fast. As for the prayers you performed while unaware of the obligation to wash the hair or to ensure water reaches the navel, there is a difference of opinion among scholars regarding the necessity of making them up. Since you are afflicted with waswasah (obsessive whispering), there is no harm for you in acting upon the opinion of those who do not obligate you to make them up.