How does a woman afflicted with coronavirus purify herself from menstruation and pray while in the hospital, given her inability to use cold water or shower, the unavailability of earth for tayammum, and her presence in a shared room?

A sick person is permitted to resort to tayammum if using water would worsen the illness or delay recovery. Tayammum can be performed on pure earth or anything covered with dust, such as a wall or a rug. If the wall is covered with wood or paint, tayammum can be performed on it if there is dust on it; otherwise, not. As for prayer, it must be performed with all its pillars, even in the presence of non-mahram men. The woman should wear loose, concealing clothes, and she must cover her entire body during prayer, including her face and hands, if non-mahram men who can see her are present.