Is it permissible or impermissible for an unmarried paternal aunt to sell her house to the questioner's brother for no charge, and to refuse to give it to her siblings after her death, and then for the brother to sell it to the questioner, and what should be done if it is impermissible?

What you referred to as a definitive sale from your paternal aunt to your brother is considered a gift (hibah). If your paternal aunt gifted the house to your brother while she was in good health and fully competent to dispose of her property, and she relinquished her control over the house, allowing your brother full disposal of it during her lifetime, then this gift is valid and enforceable. If your brother owns the house, he is permitted to sell it, and you are permitted to buy it. However, if the aunt intended to disinherit her heirs, she should not have done so, but this does not affect the validity of the gift.