Laurie/Charles appears to be the answer to each of your questions. Laurie is the protagonist (the well-rounded main character) and Charles is the antagonist (causing trouble wherever he goes. The catch, of course, is that one person is both, though we don't realize it until the end. Both are actually fairly round, dynamic characters who do nearly all the actions--both good and bad--in Shirley Jackson's "Charles." If that's the case, you can probably assume this character is the cause of everything else in the story.
One theme suggested by this story is a person's individuality. Laurie's parents didn't figure yout that Charles was a made-up person until the end because they didn't know their own child well enough. Another theme suggested by this story is gender. The parents didn't consider how Laurie would fare by giving him this name. The name Laurie is typically a girl's name. Maybe Laurie had realized he bore a girlish name so he created a boy named Charles that does all sorts of manly things.
The protagonist of the story is Laurie.The antagonist is Charles.