Is zakat obligatory on the wife's money that has not reached the nisab and on which a year has not passed, knowing that the husband takes from it when needed and adds it to his zakatable wealth? And is it permissible to give zakat to a single sick and poor relative?

A wife's money is not subject to zakat (definition) until it reaches the nisab (definition) (threshold) and a hawl (full lunar year) passes over it. She is the one responsible for paying her zakat herself, unless she deputizes her husband. It is not permissible for the husband to take his wife's money except with her permission. The husband is obligated to pay zakat on his own money, and it is permissible to give it to a needy relative whose maintenance is not obligatory upon him, especially if he is sick and cannot afford his treatment and family.