Is a woman obliged to pay the expenses of a mahram to perform the Hajj if she is less than 45 years old, and what is the ruling on refraining from doing so if the cost is exorbitant?

You are not obligated to perform Hajj and Umrah (definition) unless your wealth exceeds what is needed to pay off your debts and cover your basic necessities, such as a home, source of income, and expenses (unless your husband provides for you). If your wealth exceeds these needs, or if there is someone who sponsors you, then Hajj becomes obligatory upon you, as well as the expenses of your mahram (definition) if he does not volunteer to accompany you at his own expense. In this case, his expenses are considered part of the journey's provisions. There is also no objection to traveling with a safe group of companions without a mahram if that is possible.