She is suffering from a mental illness – how should she pray and fast?

Firstly: 

We ask Allah, may He be exalted, to heal your daughter and set her affairs straight. 

Secondly: 

If this illness is so severe that she loses consciousness during the day in Ramadan, then she does not have to make up the days that she has missed, because she is not obliged to fast in that case. 

But if the illness is only depression, and she remains conscious, then there are two scenarios: 

(i)Her sickness is one from which there is hope of recovery according to the doctors, in which case she has to make up the days that she missed when the sickness ends.

(ii)Her sickness is one from which there is no hope of recovery, in which case she is not obliged to fast, rather she should feed one poor person for each day.

Shaykh Ibn Baz (may Allah have mercy on him) was asked: There was a sick person who was not sick for part of Ramadan, then he lost consciousness and he is still unconscious. Should his sons make up the fasts on his behalf? 

He replied: 

He does not have to make up the fasts if he has lost his mind or has fallen unconscious. When he regains consciousness he does not have to make up those days. His case is like that of an insane or feeble-minded person, who does not have to make up missed fasts. But if his unconsciousness lasted only briefly, for one to two days, or three at the most, then there is nothing wrong with making up the missed fasts in order to be on the safe side. But if it lasted for longer, then he is like a feeble-minded person, and he does not have to make them up. If Allah restores his sanity then he may resume his duties. End quote from Majmoo’ Fatawa al-Shaykh Ibn Baz (15/209). 

Thirdly: 

If your daughter does not wake up to perform the prayers on time, and you cannot wake her up, there is no sin on you in sha Allah. When she wakes up she has to make up the prayers that she has missed, because the Prophet (peace and blessings of Allah be upon him) said: “Whoever forgets a prayer or sleeps and misses it, the expiation is to offer it when he remembers it.” Narrated by Muslim, 684. 

But if it is too difficult for her to offer every prayer on time, then she may join Zuhr and ‘Asr, and Maghrib and ‘Isha’, at the time of the earlier or later prayer, depending on whatever is easier for her. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

Shortening the prayers may be done only when travelling, and it is not permissible when not travelling. But joining prayers may be done in cases of need and excuses. If a person needs to, he may join prayers when travelling, whether the journey is long or short, and prayers may be joined in the case of rain and the like, and in the case of sickness, and for other reasons. The point is that the ummah be spared hardship. End quote from Majmoo’ al-Fatawa, 22/293. 

And Allah knows best.