Is it permissible to give charity to sisters who are students of knowledge, and to contribute to household expenses with the intention of charity?

If the charity is voluntary, there is no objection to giving it to sisters and contributing with it to household expenses. As for obligatory Zakat, it is permissible to give it to poor sisters if their financial support is not obligatory upon you, or to pay off a debt they owe. It is also permissible to give Zakat to a student of Islamic knowledge who dedicates their time to studying for the sake of Allah, and to a student of worldly knowledge due to their poverty or to pay off their debt. However, it is not permissible to use Zakat for household expenses. But if the husband is poor and eligible for Zakat, it is permissible to give it to him to spend as he wishes.