Is the prayer of an illiterate mother valid if her daughter stands beside her to guide her in performing the movements and to gradually teach her the recitation of Al-Fatiha, and is it permissible for this daughter to continue helping her mother in this manner?

There is no harm in you standing beside your mother to teach and instruct her in what she does not know well concerning the sayings and actions of prayer. Her prayer is valid, and many scholars have affirmed the obligation of instruction if the worshiper cannot perform the prayer except in this manner. You should be gentle with her in correcting mistakes, while explaining the importance of prayer and the danger of abandoning it. You will share in the reward of every prayer she performs.