Focusing on the second paragraph, as I think more information is needed for the first. Also, given you didn't describe how you discipline your children, don't take this as criticizing your specific discipline; instead, this is more generally "why do kids often ask why they are bad".
Many forms of discipline can very easily lead a child to internalize that he is bad. Think of it as if you're in a running class in high school. You're running every day, and your coach says "You're a slow runner. Stop running so slow. Run faster." Eventually, you'll start to believe simply that you're a slow runner. You won't believe you can fix it, and you'll just decide that you're going to be a slow runner.
Discipline with children often follows this pattern. It's very hard to work with a child who does misbehave frequently, and modify his behavior without sending the signal (either directly or not) that he is "bad". This is one of the most difficult things in parenting a strong-willed child (or, often, any child): not conveying to them the idea that there is something wrong with them internally, but that the issue is solely the behavior.
This is something covered in many, many parenting books, often with different approaches, so I would recommend that you read several and see which fits your style best. 1-2-3 Magic, Parent Effectiveness Training, many others. However, the high level overview is pretty similar across books.
Basically, it comes down to avoiding describing the child ("You") and instead describe the behavior. Instead of "You are being bad. You are hitting your sister. ", focus on what the child is doing: "Please do not hit your sister. Hitting your sister hurts her and makes me sad." This is similar to management training, if you're familiar with that.
Avoiding "You" leads both to more concrete statements of action - things the child can immediately fix - and to the child not self-identifying as "bad". Much of this misbehavior may well not be simply "being bad", also. It may be a child expressing feelings of envy, abandonment, need; or it may be wildness, caused by hunger or tiredness or simply being a little boy and feeling out his environment.
Leading back to my running metaphor, what would be useful would be if the coach instead said "Your posture is wrong; try running on the balls of your feet. Also, poor hydration can cause issues with how long you can stay out." This is what a good coach does in most cases - tells you specifically what to do differently, not focusing on the fact that you're innately slow. The same should apply to children.