These are really interesting questions Robin.
In order:
1. While I think you can add the copyright info to any document at anytime, if you were to sue someone for infringement, you wouldn’t have much of a case without official documentation. (I may be wrong though).
2. The only benefit I could see is preventing the assignments from being widespread online, where anyone can manipulate and twist the content beyond its original purpose. However, I believe this is in direct opposition of the principals of open-access: to make all information free and available to the public.
3. This is tricky. If he refuses to add the copyright, it could cause waves at work. If he adds the copyright, it denies the public from the information. However, without any legal documents, the copyright is essentially useless and can still easily be shared, so I would just add it and carry on.