AJAX Form in a Wordpress Page

<?php

if($_POST)

{
    $to_email       = "oxstew@gmail.com"; //Recipient email, Replace with own email here

    //check if its an ajax request, exit if not
    if(!isset($_SERVER['HTTP_X_REQUESTED_WITH']) AND strtolower($_SERVER['HTTP_X_REQUESTED_WITH']) != 'xmlhttprequest') {

        $output = json_encode(array( //create JSON data
            'type'=>'error', 
            'text' => 'Sorry Request must be Ajax POST'
        ));
        die($output); //exit script outputting json data
    } 

    //Sanitize input data using PHP filter_var().
    $first_name     = filter_var($_POST["first_name"], FILTER_SANITIZE_STRING);
    $surname        = filter_var($_POST["surname"], FILTER_SANITIZE_STRING);
    $surname        = filter_var($_POST["surname"], FILTER_SANITIZE_STRING);    
    $email          = filter_var($_POST["email"], FILTER_SANITIZE_EMAIL);
    $subject        = filter_var($_POST["subject"], FILTER_SANITIZE_STRING);
    $message        = filter_var($_POST["message"], FILTER_SANITIZE_STRING);


    //additional php validation
    if(strlen($first_name)<2){ // If length is less than 2 it will output JSON error.
        $output = json_encode(array('type'=>'error', 'text' => 'First name is too short or empty!'));
        die($output);
    }
    if(strlen($surname)<2){ // If length is less than 2 it will output JSON error.
        $output = json_encode(array('type'=>'error', 'text' => 'Surname is too short or empty!'));
        die($output);
    }
    if(!filter_var($email, FILTER_VALIDATE_EMAIL)){ //email validation
        $output = json_encode(array('type'=>'error', 'text' => 'Please enter a valid email!'));
        die($output);
    }
    if(strlen($subject)<3){ //check emtpy subject
        $output = json_encode(array('type'=>'error', 'text' => 'Subject is required'));
        die($output);
    }
    if(strlen($message)<3){ //check emtpy message
        $output = json_encode(array('type'=>'error', 'text' => 'Too short message! Please enter something.'));
        die($output);
    }

    //email body
    $message_body = "Regarding: ".$subject."\r\n".$message."\r\n\r\n-".$first_name." ".$surname."\r\nContact email : ".$email;

    //proceed with PHP email.
    $headers = 'From: '.$first_name."\s".$surname.'' . "\r\n" .
    'Reply-To: '.$email.'' . "\r\n" .
    'X-Mailer: PHP/' . phpversion();

    $send_mail = mail($to_email, $subject, $message_body, $headers);

    if(!$send_mail) {
        //If mail couldn't be sent output error. Check your PHP email configuration (if it ever happens)
        $output = json_encode(array('type'=>'error', 'text' => 'Could not send mail! Please check your PHP mail configuration.'));
        die($output);
    } else {
        $output = json_encode(array('type'=>'message', 'text' => 'Hi '.$first_name.' Thank you for your email'));
        die($output);
    }
}

?>