Please get him evaluated, as others have noted -- as soon as possible.
When he "throws fits" and cries and grabs his hair etc., does he seem to be doing so out of anger at the person who is telling him he's in trouble, or does he seem more to be angry at himself? Do you ever hear things from him like "I'm so dumb" or "I don't know why I did that, I didn't mean to do it, I'm stupid" and so on? In other words -- is his "fit" directed at others or at himself? That is a critical distinction and one to bring up with a professional. Neither situation is good.
Most of what you describe after that (talking in class, not doing what he's asked the first time) sounds fairly typical for his age -- but it's hard to tell because we don't know whether talking in class means a few words that get him a verbal reprimand from the teacher, or an uncontrollable urge to talk and talk despite any reprimands at all. And the thing with the note is disturbing. Most kids get blue but the note is something that would send me first to the school counselor and then to the doctor for a referral -- I would really want a psychologist who specializes in kids this age to evaluate him.