Is it permissible to give money or clothing to someone who persists in committing sins, or who uses money to purchase unlawful things, or who does not adhere to the rulings of Islamic law, such as wearing the hijab or traveling without a mahram?

You must advise your maternal aunt, admonish her, and remind her of Allah, and there is no harm in giving her money if you are certain that it will only be used in ways that please Allah. It is not permissible for a woman to travel without a mahram, so it is not permissible to invite this girl without a mahram, because her belief holds no weight, and doing so constitutes cooperation in sin.