Billing and shipping checkout fields can be removed by creating a simple plugin like the example below:
Plugin Name: Remove field
Plugin URI: http://orillacart.com
Description:Removes checkout fields
Author: OrillaCart Team
Author URI: http://orillacart.com
Save the code in your plugins directory as remove_fields.php file. New plugin should be available in WP plugins manager, activate it.After doing that, you will successfully remove the state and the country fields from the checkout form. However note that some of the fields may be used by payment and shipping plugins and the may not function correctly or at all without them.