What is the ruling on performing Hajj at my mother's expense so that I can be her mahram, knowing that she has other sons, and that she only possesses enough for her own expenses and those of her companion? And in the event that all her sons wish to accompany her, and she wishes one of them to accompany her, should the choice then be based on who has religious knowledge or who is closer to the methodology of the Salaf?

Among the conditions for Hajj to be obligatory upon a woman is her ability to cover her expenses and the expenses of her mahram. There is no objection to a woman performing Hajj at her mother's expense; in fact, it contains much good and great reward. If the mother chooses one of her sons to be her mahram for Hajj, her choice is valid even if he has less knowledge than others, because she knows best with whom she feels comfortable.