How is the ownership of stock dividends in a usurious bank calculated? And is it permissible for him to use the profits generated from these stocks for personal purposes (buying a car or household items), or for charitable purposes (building a mosque or a water well), or to pay off his outstanding debts (university expenses and government institutions)?

It is not permissible for the questioner to own the shares from his father, nor is it permissible to sell them, because they are shares in a usurious bank. The contract with the bank must be annulled, all shares returned to it, and the amount the father paid for their purchase taken and given to him.

If annulling the contract is not possible, then the returns of the shares should be examined, and the unlawful portion extracted from them and spent on the welfare of Muslims. What remains is for the father, unless he gifts it to the questioner. The questioner is not permitted to benefit from the unlawful portion unless he is poor, in which case he may take from it what is necessary for his basic needs.