Is it permissible to donate a house to a girl one is sponsoring, given the existence of heirs such as the husband, brother, and nephews, and that these heirs possess their own properties?

It is permissible for you to donate the house to that girl during your lifetime, as long as you are not suffering from a life-threatening illness. However, if the donation is made after your death, or during a life-threatening illness, it is only permissible up to one-third of your estate. If the house exceeds one-third of the estate, it is not permissible to donate the excess, and a bequest of more than one-third to a non-heir is forbidden.