My daughter suffers from congenital cerebral palsy. She hears, but cannot speak; she also cannot move or sit because of the damaged parts of her brain.
It is possible to say that she is mentally retarded. Although she is ‎now more than twelve years old, her cognitive abilities are very weak. I do not know how to tell her about the existence of Allaah The Almighty and the obligation of worshipping Him, not to mention the fast and its rulings.
Hence, I want to know whether she is considered insane and incompetent for religious assignments including the fast, or a patient with an incurable disease, whose guardian should feed a poor person for each fast day she misses.

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is known that puberty is a condition of competency for religious assignments. Reason is also another condition, as the Prophet, sallallaahu ‘alayhi wa sallam, said: “The pen is raised for three [groups of people, that is, they will not be responsible for their actions]: The insane until he becomes sane, the sleeping person until he wakes up, and the young until he reaches puberty.” [Al-Bukhari, Abu Daawood, An-Nasaa’i, At-Tirmithi and Ibn Maajah]

Hence, if your daughter has reached puberty, then she is, in principle, competent for religious assignments. The fact that she cannot talk or walk does not mean that she is insane. Consequently, the remaining factor will be sanity; if there are signs that she understands speech and responds to it correctly, then she is sane and competent for religious assignments including the fast. In such a case, if she is capable of fasting, then you should order her to fast after teaching her how to perform this act of worship and explaining its meaning and ruling to her.

If she is unable to fast and there is no hope that she would be cured, then she would have to feed a needy Muslim person for each missed day of fasting. However, feeding, if applicable, is obligatory for her (rather than her guardian) if she owns wealth.

On the other hand, if there are signs that she does not understand speech or responds to it incorrectly, then she is technically insane and not required to fast or expiate, because she is incompetent for religious assignments.

All what we have mentioned should be determined by relevant specialists.

Finally, we ask Allaah The Almighty to cure her, a cure that leaves behind no effects of the disease, and to reward you for your trial and patience.

Allaah Knows best.