what changes do Scout, Jem and Atticus go through? how does this help or hinder the characters themselves?

Mentioning each specific detail would take some time. I'm going to give you a couple of specific themes to consider. Then you can plug the details that you want in. All three characters lose a certain amount of innocence. Scout discovers that childhood ends, her brother grows up and people can let their hatred and ignorance prevail over common sense. Certainly Jem is learning what it takes to become a young man. Much of what both kids learn comes directly from Atticus. They learn not to judge others without walking a mile in their shoes and they experience this lesson first hand (Boo Radley, Mrs. Dubose). As much as Atticus is a man of the world, his belief in his friends and neighbours is shaken. Although resigned to lose this case we could see his passionate hope that perhaps the sanctity of the courts and human decency might cause people to do the right thing; they didn't. Tom Robinson is accused and he dies a short time later. I think Atticus lost a bit of innocence that day. Still, there is always hope. Atticus, Scout and Jem all know the truth affected people regardless of the verdict. All three have grown with each other.