He might be shocked at first. Since Lucius is a complex character, he could initially see it as a weakness in Harry that he could potentially use to his advantage in the wizarding world's power games.
One plot development could be Lucius using this information to try and manipulate Harry. He might offer Harry a way out of his abusive situation in exchange for Harry's loyalty or some other form of service. For example, he could ask Harry to spy on Dumbledore for him.
Well, first of all, the students would probably be shocked. His friends, like Ron and Hermione, would be extremely angry at the Dursleys. They might try to comfort Harry more often. And the school itself could start providing special resources for Harry, such as counseling or extra protection spells. Also, there could be a big change in the way the wizarding community views Harry. Instead of just seeing him as the 'Boy Who Lived', they would see him as a victim who needs support.
The other students could have a range of reactions. Some might be sympathetic and try to befriend Harry more. Others might be afraid, especially if the abuser is still around. But overall, it would create a stir in the wizarding community, and there would be a general outpouring of concern for Harry's well - being.
The abuser might face the wrath of the DA. They could be ostracized within the wizarding community. The DA members could use their influence to make sure the abuser is held accountable for their actions.
Well, if we consider the 'umbridge finds out harry was abused fanfiction', it really depends on the writer's take. One possibility is that Umbridge, being the power - hungry character she is, might try to cover it up to maintain the status quo at Hogwarts. On the other hand, she could also see it as a way to discredit Dumbledore, thinking he failed to protect Harry. There's also a chance that the discovery could lead to a change in Umbridge's relationship with Harry, from being a tormentor to an unexpected ally, though this would be a huge shift in her personality.
Their friendship would become deeper. Ron would be more protective and more attuned to Harry's emotions. There would be a new level of trust as Harry has shared such a difficult and personal experience with Ron.