Am I obligated to maintain ties with my father through financial support and affection, given that he abandoned me as a child and did not spend on me, and he mistreats his wife, shows ill manners towards God, and behaves improperly? And does he have any right over me under these circumstances?

The father's right is not forfeited by his wrongdoing, lack of financial support, or falling into sins. He must be honored and obeyed in matters that do not involve disobedience (to God). One must also treat him kindly, advise him, and provide for him if he is poor and in need, unless he has apostatized. If he apostatizes from Islam, then his maintenance is not obligatory. If one fears that the money will be spent on sins, then the provider can purchase household necessities himself.