Is it permissible for a woman to perform Umrah with her husband's 17-year-old son as her mahram, and can a child be brought along with them with the intention of instilling religious values in him? And is it permissible for a woman to perform Umrah on behalf of her parents?

The husband's son is a mahram (unmarriageable kin) because of Allah's saying: "And do not marry those [women] whom your fathers married." It is permissible for a woman to travel with him to perform Umrah, and she does not need a child with them. Performing Umrah on behalf of one's parents is permissible, as evinced by the Hadith of the Khath'amiyyah woman whom the Prophet (peace be upon him) permitted to perform Hajj on behalf of her father.