What should I do about my money, which is mixed with unlawful (haram) earnings due to my father's dealings with usurious banks? What are the steps to purify this money after repentance, and is it permissible for me to live under his care if he does not repent?

You must advise your father to repent and withdraw his money from usurious banks, clarifying the danger of dealing with usury, citing Quranic verses and prophetic hadiths that warn against it and promise its practitioners war from Allah. A complete repentance includes spending the usurious gains on Muslim welfare. Regarding the ruling on him spending on you, if the expenditure is directly from usurious money, it is not permissible for you to accept it except in a state of dire necessity. If his lawful money is mixed with unlawful money, there is no harm in accepting his expenditure to the extent of the lawful amount.