Is the prayer valid for an elderly woman who has memorized only half of Al-Fatiha and prays while sitting?

She must learn Al-Fatiha. If she is unable and only memorizes one verse, she should repeat it seven times. If she has memorized more, she should repeat it a number of times equivalent to the seven verses of Al-Fatiha. If she is unable to recite any part of Al-Fatiha but can recite something from the Quran, she should recite an equivalent amount to Al-Fatiha.

If she is unable to recite anything from the Quran, she should say: "Subhan Allah, wal-hamdu Lillah, wa la ilaha illa Allah, wa Allahu Akbar, wa la hawla wa la quwwata illa billah." (Glory be to Allah, and praise be to Allah, and there is no god but Allah, and Allah is the Greatest, and there is no might nor power except with Allah).

As for her praying while sitting, that is obligatory for her if she is unable to stand, and she should gesture for bowing and prostration if she is unable to perform them.

We advise you to strive in honoring her and showing kindness to her, to seize the opportunity of her life, and to advise her gently and kindly regarding what is necessary for her, and to be keen on her satisfaction by all possible means, for the satisfaction of the Lord is in the satisfaction of the parent.