In my registration form I need to add the Country field. I would like to use the built-in countries dropdown of Magento. Via backend it is not possible to add it. How should I add it?
You can search in this site or google how to add customer attribute. The specific for you case is that your attribute should be with:
'type' => 'varchar', 'input' => 'select', 'source' => 'customer/entity_address_attribute_source_country',