Are the profits resulting from a sum of money deposited by the paternal uncle into his nephew's account—to avoid deductions from his own account due to problems with his wife—the right of the uncle or his nephew, knowing that the deposit was made in an Islamic bank and the Dar Al-Ifta (Fatwa Council) has issued a fatwa permitting the taking of profits from it?

As long as the account is a savings account, the bank speculates with the money and shares the profit with the depositor. What the questioner mentioned means that his uncle deposited the amount in the questioner's account for himself, so the profit and the guarantee revert to the uncle. Therefore, it is not permissible for the questioner to take anything from the profit except with his uncle's permission, and the way for him to be entitled to the profit is to take the amount as a loan from his uncle.