What is the ruling regarding my mother's prayer, as she is unable to perform it correctly, forgets her invocations, and makes mistakes in reciting Al-Fatiha despite her ability to pronounce the emphasis (tashdeed)? She does not master Arabic and forgets what she has learned. What are the simple formulas she can memorize for her prayer?

It appears your mother suffers from severe memory impairment and forgets matters related to prayer. Therefore, help her as much as you can. For what your mother is unable to recite of adhkar (remembrances) and the like, there is no blame upon her, for the Prophet, peace and blessings be upon him, said: "When I forbid you from something, avoid it. And when I command you with something, do as much of it as you can." Some adhkar, such as the remembrances of bowing (rukūʿ), prostration (sujūd), and between the two prostrations, are considered sunan (recommended acts) by the majority of scholars, and prayer is not invalidated by omitting them. As for omitting the tashdīd (doubling) of the letter yāʾ in "iyyāka" (in Al-Fātiḥah), there is a difference of opinion regarding it, and your mother is permitted to follow those who do not consider the prayer invalidated by that. Prayer only has its known form, but your mother can limit herself to Al-Fātiḥah, and a single instance of tasbīḥ (glorification) in bowing and prostration, and "Rabb ighfir lī" (My Lord, forgive me) between the two prostrations.