Is it permissible to donate the reward of reciting Surat Al-Kahf on Friday to a mother who does not read, and would she be included in the Hadith "a light between the two Fridays" in this case? And does that apply to a father who can read and write if the reward is also donated to him?

Donating the reward of acts of worship, such as reading the Qur’an, to the living is a matter of scholarly disagreement. The Hanbalis permit it for any Muslim, whether living or deceased. Others, including Ibn ‘Uthaymin, hold that the living do not benefit from this except in specific cases, such as performing Hajj on behalf of someone unable to do so, and that this was not a practice known among the righteous predecessors. Accordingly, donating the reward of reading Surat al-Kahf to your living parents is permissible according to the Hanbalis, but not permissible according to others.