Is a 13-year-old son considered a mahram for a woman, and is her 'Umrah valid if she goes to the Haram with him?

It is impermissible for a woman to travel without a mature, sane, trustworthy mahram, due to the Prophet's (peace be upon him) saying: "It is not lawful for a woman who believes in Allah and the Last Day to travel for a distance of a day and a night, except with a mahram." However, after arriving at her place of residence, she may go out alone as long as she does not fear harm. If she does, she should seek assistance from her relatives who are with her. The conditions for a mahram in travel are not required for these relatives. The 'Umrah is valid if it fulfills its pillars and obligations.