Is it permissible to perform Hajj on behalf of a sister who passed away at the age of 34, having suffered from cerebral palsy since birth and been bedridden? And what is the ruling regarding prayer, fasting, and Zakat on her behalf?

If the sister is of unsound mind, Hajj, prayer, and fasting are not obligatory upon her, because sanity is the basis of obligation (taklif). Zakat must be paid from her wealth if she owns any.

If she was sane and passed away without performing Hajj, there is a detailed explanation: - For one who died after having the ability to perform Hajj but did not, Hajj should be performed on their behalf from their wealth, provided that the proxy has already performed Hajj for themselves. - For one who was financially capable but physically unable due to illness, and could not be transported to perform Hajj, their ruling is the same as the previous case. - For one who did not have the ability due to poverty or chronic illness and died before performing Hajj and left no wealth, there is nothing upon them, and the heirs are not obligated to perform Hajj on their behalf. However, if one of her siblings voluntarily performs Hajj on her behalf, it is permissible.

Regarding Zakat for the deceased: - If they left wealth and Zakat had become obligatory upon it, it must be paid from the principal amount, because it is a debt upon them. - If they passed away before Zakat became obligatory upon them, ownership of the wealth transfers to the heirs, and its Zakat becomes their responsibility. - If the deceased did not leave any wealth and their family voluntarily gives charity on their behalf, it is permissible, and the reward reaches them.

Regarding prayer for the deceased: - It is not legislated for anyone else to perform obligatory prayers on their behalf. - Regarding dedicating the reward of voluntary prayers: Scholars have differed on this. Some have preferred that the reward reaches the deceased (such as Ibn al-Qayyim), while others have preferred that it does not (such as al-Nawawi and Ibn Abd al-Barr).

Regarding fasting for the deceased: - For a sick person who was unable to make up missed fasts until they died, making up the fasts on their behalf is not required by agreement. - If they were able to make up the fasts but did not do so until they died, it is legislated to make them up on their behalf, according to the preponderant opinion. - Some scholars permitted dedicating the reward of voluntary fasting to the deceased.