There are a lot of things confused here.
For the beginning, as recommended in the editor’s comment on the “Add JS Code” page, you’ll need to wrap your JS code in
jQuery(document).ready(function($) {
\\ your code
});
because of the jQuery noconflict mode used by default in WordPress (see this article).
Then, the “url” cannot simply be a PHP file in your public_html folder, but it has to be WordPress built in AJAX url: /wp-admin/admin-ajax.php (see this article).
Afterwards you can write a function hooked in the “wp_ajax_test” and “wp_ajax_nopriv_test” WP actions where you can process the $_POST variable sent by your AJAX code. The WP actions are called “wp_ajax_test” and “wp_ajax_nopriv_test” because you’ve set your “action” variable to “test”. They might also be called “wp_ajax_my_ajax_action” and “wp_ajax_nopriv_my_ajax_action” if you set your “action” variable to “my_ajax_action”.
If you have more questions, please consider asking them on stackoverflow. Your issue is not related to this plugin directly, but generally to your understanding of the WordPress AJAX principles.