However, C&D's don't really carry any legal weight in the US to my knowledge... but I don't see any harm in complying ahead of time just to be safe. The only "damage" I can see is just by nature of the service being down temporarily.
If there is even a possibility that a court may find the service violating a law, I think the legal advisor would likely say to just leave the service down unless you have many tens or hundreds of thousands of dollars or more to fight it... you can most likely avoid the entire lawsuit altogether just by complying with the C&D. And this kind of suit is one that can easily ruin your company or even personal life... so avoiding it seems smart.
> Anyone can send an request.
As for emails, I think BIMI has solved this for some time now, at least for large companies.