Can my elderly mother, who cannot read or write, earn the reward for reciting the Quran by opening the Mus'haf, pointing to the verses, and reciting a short Surah, or by repeating "La ilaha illa Allah" from the beginning of the Surah to its end?

Looking at the Mushaf (definition) is an act of worship, and reading from it is better than reciting by heart because it combines reading and looking, and it is an independent act of worship. There is no objection to the mother looking at the Mushaf, whether she opens it to the place where she is reading or elsewhere. It is better for her to open it to the place of reading so that she gets accustomed to locating the surahs. However, opening the Mushaf and running one's finger over its verses with the intention of gaining the reward of reading the entire Mushaf while only reading a part of it or reciting adhkar, is not appropriate.