While ADHD cannot be ruled out on the basis of what you have described, it alone would not account for all of these problems. It sounds like your son is a
brightBright beginnings child who displays a range of behavioral issues. The prudent thing to do is arrange an evaluation with a pediatric mental health clinician who can figure out the ADHD (possibly) piece, as well as the other problems. It may be that the most important intervention will be a systematic behavioral system, but that can be determined as part of the mental health evaluation. The earlier you figure this out the better. These problems are not within the normal spectrum for a child of six; they invite professional help.