Is it permissible to give zakat to an unmarried brother to help him marry, and to sisters, and is it permissible for the mother to save it for their marriage?

It is not permissible to give Zakat to the mother at all, because her maintenance is obligatory if she is poor; otherwise, she is not eligible for Zakat. The same applies to sisters if they are not poor. As for a poor brother, there is no harm in giving him Zakat to help him get married, because it is a sufficiency for those who need it.