Is it permissible for the questioner to spend from his profits on his maternal aunt who intends to perform Hajj but does not possess sufficient money to fulfill the obligation, and is it permissible to give her from the zakat of his wealth?

Spending ill-gotten wealth—including bank interest—should be for general Muslim welfare or for the poor and needy. Therefore, do not pay this interest to your aunt for her Hajj, as this is not among its legitimate expenditures. As for paying zakat money to her for this purpose, there is a difference of opinion among scholars, and the majority prohibit it.