Is it permissible to give zakat on gold and silver to a close relative who is a widow, owns and resides in her home, and has her daily sustenance, or is it better to seek out someone more in need than her?

If the woman is poor—meaning her income is not sufficient for her needs—and you are not obligated to spend on her, then it is permissible to give her from the Zakat. In fact, she is more deserving, according to the hadith: "Charity given to the poor is a charity, and charity given to a relative is both charity and upholding the ties of kinship."