She suffered a brain injury at birth; does she have to pray and fast?

I have a sister who is 25 years old, and she was born with a disability which means that she is quadriplegic, in addition to which she is unable to speak. From infancy she has been disabled and is unable to eat or drink or go to the toilet by herself, so her mother feeds her, gives her drinks and takes her to the toilet. She is also unable to move her arms. On the intellectual side she understands things very well, she feels joy and sorrow, she recognises people, tells the time and listens to the Qur'aan. My question is: does she have to do perform all the obligatory duties such as prayer, fasting and Hajj, even though she is unable to do wudoo’ and does memorise any Qur'aan and is not able to do so, and she is not able to sit and move during the prayer? I have tried many times to teach her how to pray, but she does not know the number of rak’ahs and she forgets and makes mistakes, and turns to the right and left, and sometimes she laughs involuntarily. And what about fasting? Should she fast or not? Or should she abstain from fasting and should charity be given on her behalf?.