ANSWER:

If she saw her purity before the break of dawn and NOT before sunrise, she can intend to fast and this is valid as performing ghusul has nothing to do with her fasting.

As for prayers and uplifting her major ritual impurity, she must perform ghusul. If she is unable, she can perform tayammum instead of that. If she is totally paralyzed, she can pray without ghusul or tayammum due to inability and she must pray the way she can. 

I’ve read that if a woman is sure that her menstruation is over before sunrise, and she intends to fast, her fast will be valid even if she delays ghusl until morning. But what if she isn’t able to do ghusl even in the morning or throughout the day because of an illness e.g. high fever? Is her fast valid? What about the prayers throughout the day?