no, the school cannot tell other parents about a child's sn (or any other information for that matter).
If the strategies that the school have given the children seem to be working, then I would be inclined to leave it at that for now. And while telling a child to hit back might not be the preferred method of dealing with the issue, I can see (and I realize I might get flamed for this) why a parent might advise a child who is constantly being hit to hit back. As I said it's not right, but I can see how a parent might reach that point.
I wouldn't automatically assume the child has sn purely because he is violent. There is a very violent child in my ds' class, and he does not have sn, but he does have other issues at home which do contribute to the way he behaves.
Perhaps you could befriend this child's mum at the school gate? After all if her child is seen as the troublemaker, she might appreciate a friend.