Are we obligated to pay the debts of a father resulting from fraud and deception, especially those for which the creditors have no proof? And how do we deal with a father who commits deliberate and shameful acts to provoke his children, given that doctors confirm his mental soundness?

If someone, being of sound mind, reviles the Creator or the Messengers, or mocks the rituals of religion, he commits an act of disbelief (kufr), and his wife is separated from him. He has no claim over her until he returns to Islam. If he is of unsound mind, then he is not held accountable. You are not obliged to pay his debts from your own money, but it is commendable to pay them if it does not cause you hardship and if he did not use them for amusement or falsehood. It is obligatory to treat your father kindly and dutifully, and to try to reform him. It is not permissible for a son to strike or curse his father, but he may prevent him from disgraceful acts.