No, a minor should not have a right to privacy as minors are not yet old enough to understand that there are many things a minor should not do. As a result, a minor's parents should have the right to know what a minor is doing at any given time.
As long as a parent is paying for the vast majority of his/her child's expenses and responsible for the child's actions the parent has a right to know what is going on in that child's life. I think in general parents choose to allow their kids some degree of privacy, but I think that's a privilege, not a right and if the kid abuses the privilege, the parents can take it away. Teachers and other adults shouldn't be allowed to invade a kid's privacy, but parents may.