Is it permissible to deposit money in a usurious bank and take its interest to give it away as charity while continuing to pay zakat, given the unavailability of a nearby Islamic bank and the fear of theft if the money is kept at home?

It is not permissible to deposit money in a usurious bank, even if you donate the interest, rather it must be deposited in a reliable Islamic bank. The existence of an Islamic bank does not permit depositing money in a usurious bank. It is only permissible to deposit money in a usurious bank in cases of extreme necessity, such as fear of theft or usurpation, and this should only be in a current account. The fear of theft when going to the bank is not a legitimate necessity.