Is it permissible to perform Hajj without the parents' permission, and is Hajj valid, as is going out seeking knowledge, and are they sinful for preventing it?

Parents can prevent their child from performing a supererogatory Hajj, and they will not be sinful for that. However, they cannot prevent him from performing the obligatory Hajj, and they would be sinful if they did. The child's Hajj is valid in all cases, even if he is disobedient in the supererogatory Hajj. He may also travel to seek knowledge without his parents' permission.