Should the surplus from the deceased mother's money in the bank be given out, and is the mother sinful for not giving it out, given the son's need for that surplus?

Any increase on a deposit in a usurious bank is considered Riba (usury) and is not permissible for the owner of the deposit nor for their heir. The heirs are obligated to spend this usurious interest on charitable causes and for the benefit of Muslims. If the heir is poor and in need, there is no harm in them taking from it according to their need. The deceased sinned when entering into the usurious contract, and after their death, the heirs are responsible for disposing of the unlawful money according to Islamic law.