Edmund Hooper
Edmund is the only child of Joseph Hooper, who has inherited a large house which Edmund has never been particularly fond of but when another child moves into the house, along with his mother, Edmund finds that he wants to protect his rights to the house, and also drive home the fact that it is his family's house, Charles just happens to live there.
Edmund is quite a cold fish, but this is largely because his father is cold as well. They have as distant a relationship as a father and son can have, but this thaws slightly when Charles and his mother move in to live with them and they spend more time together on outings and excursions.
Although Edmund bullies Charles, it is he who is actually physically harmed in the course of the relationship between the two, when Charles pushes him from the side of the castle walls. Because this makes him seem like the victime, not the aggressor, in their relationship, he is able to manipulate the situation to his own advantage and garner sympathy not only from his father but from Charles' mother as well.
As readers, we are not supposed to like Edmund. He is a spiteful, jealous boy who drives Charles to suicide, but in many ways he is also a victim himself. He does not get much love from his father, so it is natural that he would want to cling onto it for himself. Because he doesn't get love or affection he clings also to the things that he does have, material things, like his family home. He does not want to share them with Charles, whom he sees as an interloper, and as a child who seems to be getting more affection from his father than Edmund. His life as a child has not been much fun, and consequently he has become a person filled with envy and anger. Having never really been encouraged to have much of a social life - there were never any playdates at Warings - he is also socially awkward and unable to read social cues correctly.
Charles Kingshaw
The last thing Charles actually wanted was for his mother and Edmund's father to become romantically intertwined. He is not happy living at Warings and feels both out of place and unwelcome, but he starts to really gain in confidence when he leaves the confines of the house and ventures into the local town. He makes friends easily, understands appropriate social cues and shows himself to be a popular boy. His new friendship with Fielding enables him to enjoy life around him rather than being confined to Warings which he finds doom-filled and oppressive.
Charles is bullied relentlessly by Edmund, not generally physically, in a way that he could use as evidence of the bullying,but emotionally. He knows that if they attend the same school Edmund will make his life a misery.He is so scared of him and so filled with horror that his mother has forced him to spend the rest of his childhood growing up alongside his tormentor that he kills himself by walking into the lake and drowning.
Joseph Hooper
Hooper comes from the "children should be seen and not heard" school of parenting. He is a cold man who largely left the raising of Edmund to his wife. When she passes away, there is no relationship between father and son to speak of, and they are more like strangers living in the same house than they are a solid family unit.
Ironically, Joseph seems to think that bringing another young boy into the house will remedy this. In actual fact it makes everything worse, which was predictable - after all, Edmund gets little enough affection from his father before Charles arrives; why would Joseph think he wants to share the little affection that he gets? Joseph is not a bad man, but he is a fairly clueless father, and has a tendency to see what he wants to see in a situation rather than the situation as it is. For example, both he and Charles' mother want the boys to get along so that they can get married and live as a happy family. They choose to marvel at the wonderful way in which the boys are interacting because it is more convenient for them to do so. Joseph has a tendency to see things in their most convenient light, rather than in their reality.
Helena Kingshaw
When Helena moves into Warings with her son in tow, it is ostensibly in the role of housekeeper, although it is unclear whether or not the two were romantically connected prior to this and hiding behind the propriety of an employer/employee arrangement. Helena is a happy, glass-half-full kind of person who loves her son and has a good relationship with him. She also hopes to have this kind of close maternal relationship with Edmund, and believes this is what she is achieving, unable to see that Edmund is actually manipulating her rather than treating her with genuine affection.
Helena is so intent upon making sure that the boys appear to get along that she does not actually see what is actually happening to her own son. Although his personality is changing and he is withdrawing terribly, she is not noticing this because she really doesn't want to. Although she loves her son, she does not want to consider the possibility that staying at Warings forever might not be the best thing for him.