What is the age a محرم must reach to travel with a woman, and is it permissible to travel with a 13-year-old younger brother if he is the only available male محرم?

A Muslim must obey Allah's commands and not pay attention to people's sayings. The mahram with whom a woman travels must be an adult, because the purpose of the mahram is to protect and safeguard the woman, which cannot be achieved by a non-adult. A male becomes mukallaf (accountable) and thus eligible to be a mahram if he reaches the age of fifteen, or ejaculates with desire, or grows coarse hair around the private parts.