What is the better way to implement Auth0 for my multi-country site?

Your requirement to allow users to register multiple times in different countries means that you will need to use multiple connections. One way you could structure it is to have a client (application) per country, with it’s corresponding connection. E.g.

Application1 > Connection1
Application2 > Connection2

This way, a user who registers with application1 (using Connection1), can also register for application2 (using Connection2) with the same email address.