Does what the questioner spent on her husband, her children, her sick father, her brother's family, sponsoring an orphan, and various charities count as Zakat, or is she still required to pay Zakat on her wealth?

There is no zakat due on your salary if you spend it entirely on your children, husband, and relatives, and you do not save from it an amount that reaches the nisab and a hawl (full lunar year) passes over it. Zakat becomes obligatory on savings from the salary if it reaches the nisab (85 grams of gold or 595 grams of silver) and a hawl passes over it, and the amount of zakat due is a quarter of a tenth (2.5%). It is permissible to pay zakat in installments as monthly aid to the poor before it becomes due (advance payment of zakat), but it is not permissible to pay it in installments after it becomes due; rather, it must be paid immediately. It is not permissible to give zakat to a poor father if his maintenance is obligatory upon you, and what you give to your brother who takes care of your father cannot be considered from zakat if it is a compensation for him. Sponsoring orphans from zakat is permissible if they are poor and have no provider.