What is the ruling on a father disowning his daughter because she informed him of his secret marriage, and is it permissible to inform him of this despite knowing his stubbornness and tendency to disown? What is the ruling on supplicating against a stepmother whose marriage is not documented, and is it permissible to accuse her of adultery in this case?

The fundamental principle is the permissibility of polygyny, within the Sharia-compliant frameworks, for whoever is capable of it. One should not condemn a father who marries a second wife, nor is it permissible to seek out the private matters (awrah) of his second wife, or to invoke curses upon her, or accuse her of adultery. It is obligatory to honor and be good to one's father. It is not permissible to accuse him of adultery without clear proof, or to mistreat him. If your father cuts ties with you without cause, you are not considered disobedient unless you reciprocate his action or fall short in honoring and respecting him.