AJAX Register - does it replace the default registration form?

I would like to know if the AJAX register replace the default registration form and is there any opportunity to add users via that AJAX Register?

And if I am doing a website on a localhost (due to testing reasons) and after that transfer it to the web-server, does the license is going to be transferred as well or I have to buy another one?

Yes, it replaces default registration form, as DEMO shows: joomla25.sakic.net/users/registration/

Users register yourselves. If you want to add them manually you do that in Joomla admin, users management, just as without AJAX Register.

Yes, it will work both on localhost and final domain, no problem.