If a son is treated poorly by his father, backbites his mother, and cannot be advised, is he absolved of sin if he seeks forgiveness in his heart without being answered, or must he do something else? And is it forbidden for the son to supplicate against his father in this situation?

If advising a parent against backbiting would cause greater harm or corruption, then there is no sin in remaining silent while disapproving in one's heart. It is not permissible to supplicate against a parent; rather, one must supplicate for their guidance and righteousness, no matter how much they have wronged.