You are using the user email confirmation option, so to checkout the customer needs to activate his account by clicking on a link in the email.
Now that the system messages are displayed, the user is informed.
Concerning the doubled checkout page, I think that you have a problem with your template.
The save option is working fine, when clicking on "register". And to have the "next" button, the customer need a valid account, else he can't checkout.
You can change the option to "no validation" for the new user registration in the joomla user options.