No, no permission needed for any of those things.
I view it as a bit like being faithful. In a trusting relationship you both know what expectations you have of each other in terms of monogamy. If one cheats then it may be a dealbreaker, and may end the relationship, but we should not legislate the terms of a relationship.
I know that it would be a massive issue in our relationship if I donated eggs or if DH donated sperm. We both agree that we would not wish each other to do that.
I don't need a law to stop him from doing that. I trust that he won't, and if he broke that trust we would have big problems. A relationship is about choosing to do right by your partner - not being mandated to do so.