Does the difficulty (haraj) fall away from my grandmother due to her old age, knowing that she does not complete her prayers correctly, such as not completing Surat An-Nas, and not straightening up after prostration and during the tashahhud?

If the grandmother is of sound mind, prayer is not waived for her due to old age. She must perform as much of the pillars as she is able. Reciting a surah (definition) after Al-Fatihah is a Sunnah (definition), and omitting it does not invalidate the prayer. If the grandmother recites Al-Fatihah, that is sufficient for the validity of her prayer. If she is unable to learn Al-Fatihah, she should say: "Subhan Allah, walhamdulillah, 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)." Tranquility upon rising from prostration and in all other physical pillars is a rukn (integral part), and its meaning is the stillness and settling of the limbs. The final Tashahhud (definition) is a rukn in prayer. If the grandmother does not observe tranquility in her prayer or omits the Tashahhud, she must be advised regarding that. As for standing in prayer, if she is unable to do so, it is waived for her.