Is it obligatory for children to pay off their father's debts accumulated from wrongfully taking people's money, buying cars, and borrowing from banks without repayment, whether during his lifetime or after his death, especially with his continued sin and spending his salary only on himself?

You are not obligated to pay your father's debt as long as he is alive, especially if his debt is due to extravagance, as this would be considered assisting him in sin. However, it is advisable to pay his debt after his death to free his soul, based on the Prophet's (peace be upon him) saying: "The soul of a believer remains suspended by his debt until it is paid off on his behalf."