Do Internet users have rights? Which? Should there be laws, just for the Internet, that go beyond national laws? Why?

Yes. When you create an account on a website, you agree to follow certain rules set by the website. You also agree to give the website some information (Birthdates, Phone Number, Address). However, if the website missuses that information, such as leaking private information, then the users right of privacy has been violated. Unless the user specially agreed that their information could be used in such a way. There should laws for the internet that apply only to it, as it is a unique environment and normal laws can't be put in place, such as in a city.