Is it permissible to give zakat to the indebted sister who borrows money to pay installments on her house, is about to get married, and is planning an extravagant wedding, knowing that she lives with the zakat payer, who covers the household expenses?

It is permissible to give Zakat (definition) to a needy sister, even if she lives with the Zakat-giver, as long as the Zakat is not spent on the household expenses of the Zakat-giver; in that case, it is not permissible. The Zakat-giver should advise his sister to abandon extravagance and wastefulness in marriage.