Is it permissible for my grandmother to pray with gestures, tasbeeh, and takbeer only, without the opening takbeer and reciting Al-Fatiha and the rest of the pillars and obligations, given her health conditions of hearing impairment and difficulty in understanding? And are there other deeds I can do for her to earn reward while she is still alive?

Prayer holds a great status in Islam, and it is the first act of a Muslim that will be examined on the Day of Judgment. A severe warning has been mentioned for those who neglect it or waste it. Prayer is not waived for a person as long as they retain their sanity. Your grandmother must make up all the prayers she missed. If she does not know their exact number, she should continue making them up until she is reasonably certain that her obligation has been fulfilled. If she is in a state of incapacity and difficulty, she should pray according to her ability. If she is unable to recite Al-Fatiha, she should follow an Imam or suffice with remembrances (dhikr). If she is unable to perform some pillars, such as standing, she should pray sitting, or lying down, or by gesturing. Prayer is not waived for her as long as she retains her sanity. Among the acts whose reward will benefit her in her life is giving charity with the intention of dedicating its reward to her.