Is this boy Schizophrenic?

We think this kid in my class has a problem. It started when he moved here, he was kind of off-set by human contacts and started becoming irritable thought his time. He will stare at one place for a irrational amount of time, as if in a black Aura or daze. When you talk to him he's shake uncontrollably and ask what you said because he never knows. He never pays one thing attention for long periods of time and believes in conspiracy. He is mean to everyone except for me, Sara. He yelled at my friend for sitting next to me (His believed god-given spot at the lunch table) and will constantly follow me. He peed his pants twice in the last week. He becomes aggravated by questions of old friends and old town/family. He tries to make conversation shorter than needed. He likes to talk and fight with himself, jerking his arms in a flailing fashion. But, can you help diagnose him?