WordPress AJAX for contact_me form

Question

I have converted this template into a WordPress theme. Everything works successfully except I can't get the correct url for the AJAX request in the contact_me.js section.

 $.ajax({
            url: "././mail/contact_me.php",
            type: "POST",
            data: {
                name: name,
                phone: phone,
                email: email,
                message: message
            },
            cache: false,
            success: function() {
                // Success message
                $('#success').html("<div class='alert alert-success'>");
                $('#success > .alert-success').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                    .append("</button>");
                $('#success > .alert-success')
                    .append("<strong>Your message has been sent. </strong>");
                $('#success > .alert-success')
                    .append('</div>');

                //clear all fields
                $('#contactForm').trigger("reset");
            },
            error: function() {
                // Fail message
                $('#success').html("<div class='alert alert-danger'>");
                $('#success > .alert-danger').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                    .append("</button>");
                $('#success > .alert-danger').append("<strong>Sorry " + firstName + ", it seems that my mail server is not responding. Please try again later!");
                $('#success > .alert-danger').append('</div>');
                //clear all fields
                $('#contactForm').trigger("reset");
            },
        })
    },

I know it has to do with the way the files in WordPress are referenced. I have done similar things when adding js files in the HTML but I am not sure how to handle it in the js file.

EDIT: Maybe I have to add the code from contact_me.php to an ajax callback in functions.php?

EDIT 2 Here is my send_form which doesn't seem to be sending any mails.

function send_feedback(){
// Check for empty fields
if(empty($_POST['email'])       ||
    empty($_POST['message'])    ||
    !filter_var($_POST['email'],FILTER_VALIDATE_EMAIL))
{
    echo "No arguments Provided!";
    return false;
}

$email_address = $_POST['email'];
$message = $_POST['message'];

// Create the email and send the message
    $to = 'xyz@mydomain.io'; // Add your email address inbetween the '' replacing yourname@yourdomain.com - This is where the form will send a message to.
    $email_subject = "Demo Feedback Form:  $email_address";
    $email_body = "You have received a new message from your demo feedback form.\n\n"."Here are the details:\n\nEmail: $email_address\n\nMessage:\n$message";
    $headers = "From: noreply@mydomain.io\n"; // This is the email address the generated message will be from. We recommend using something like noreply@yourdomain.com.
    $headers .= "Reply-To: $email_address";
    mail($to,$email_subject,$email_body,$headers);
    return true;
}
add_action('wp_ajax_nopriv_send_feedback', 'send_feedback');
add_action('wp_ajax_send_feedback', 'send_feedback');

Answer 1

add in your header.php

<script>var ajaxURL = '<?php echo esc_js(admin_url('admin-ajax.php'));?>';</script>

add in your url: ajaxURL

in your case

    $.ajax({
                        url: ajaxURL,
                        type: "POST",
                        data: {
                            action: 'send_form',
                            name: name,
                            phone: phone,
                            email: email,
                            message: message

                        },

in your functions.php

    function send_form(){
    $name = $_POST['name'];
    $phone = $_POST['phone'];
    $email = $_POST['email'];
    $message = $_POST['message'];

    //Do your send mail function etc.

    wp_die();
    }
add_action('wp_ajax_nopriv_send_form', 'send_form');
add_action('wp_ajax_send_form', 'send_form');