What is the ruling of the Shari'ah on how to deal with a debt owed by a mother suffering from memory loss, and is it necessary to document the waiver of the debt with witnesses? And what is the ruling on executing the mother's will to hold a lunch after her death?

What the mother mentioned does not clear her liability from the debt, because she made the absolution contingent upon her death, and this is considered a bequest to an heir, which is not enforceable without the consent of the other heirs. As for the bequest of the lunch, please refer to Fatwa No. 115771 for details. And the mother's favoritism towards her son regarding the house rent is considered a gift, which is permissible if there is a legitimate reason for it, otherwise it is not permissible.