Is it permissible to disown a father who commits abominable acts, does not follow the Sunnah, curses his children, believes his words are like the Quran, mistreats his daughters, and seeks out their private matters, despite being a believer who prays and fasts?

There is no objection to supplicating with "al-Lutf" (Gentleness/Kindness), as it is one of Allah's Beautiful Names, and it may be a cause for alleviating divine decree. However, we do not know of anything specifically reported concerning it. The obligation is to invite the father with kindness, to not raise one's voice at him, to show him filial piety and benevolence, even if he is disobedient, for Allah has commanded filial piety towards even polytheist parents. The acceptance of deeds is up to Allah, but disobedience (to parents) may prevent their acceptance. As for disavowal, it should be from the unrighteous deed, not from the parent himself, while still fulfilling the obligation of showing him filial piety.