D.K.
It sounds like he is a perfectly normal 4 (girl or boy). The job of a 4 year old is to play - that's how little kids learn about the world. Running around and rough housing are also perfectly normal. Setting some limits (eg - no pushing or hitting) should be acceptable and I would think he is old enough to understand that but he needs activity. It is also normal for him to blame everything on other people. He probably gets frustrated when he can't do something yet and is still developing impulse control. How does the teacher interact with him? Does she make eye contact, touch him on the shoulder and make a connection when she asks him to do something? Or does she announce to the class whatever it is and assume everyone can immediately stop what they are engrossed in to listen? You might just ask him why he doesn't paint - it could be something simple - he doesn't like how the paints smell or the teacher yelled at him one day because he was messy.