Are the obligatory duties, such as prayer, fasting, and Hajj, incumbent upon a sister who suffers from quadriplegic cerebral palsy, is unable to move, speak, perform ablution, or memorize the Qur'an, and forgets and is absent-minded while attempting to teach her how to pray?

If the sister does not comprehend the meaning of prayer and its method, nor the reality of fasting and its requirements, then she is not held accountable due to her mental incapacity. This is based on the saying of the Prophet, peace and blessings be upon him: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane person until he regains his sanity." Since she is not held accountable, there is no obligation to feed the poor on her behalf as compensation for fasting.