Does Allah accept supererogatory fasting from a person who has animosity toward his brother, knowing that the other party is the one in error? And does fasting become void if the fasting person wrongs someone and then seeks forgiveness?

Animosity between Muslims delays the forgiveness of sins. If it exists between one person and his brother, it causes the delay of forgiveness for both until they reconcile. Once they reconcile, Allah forgives them the sins that were between them. A fast observed by someone who has animosity with his brother is valid and sufficient, but its acceptance by Allah depends on his sincerity and intention. Reconciling disputes (islaah dhaat al-bayn) is better than supererogatory acts of worship, because corruption of relations shaves away religion. As for backbiting others, it is a major sin, and its ugliness increases during fasting, diminishing the reward. However, it does not invalidate the fast according to the majority of scholars.