your form tag:
<form name="contact_us" id="contact_us">
does not set a method. by leaving the method blank, it will use the GET method, but UE is expecting the for it to use the Post method.
you need to set the method to post. also, you should set the forms action, you should set the action of the form to post to itself:
<form name="contact_us" id="contact_us" method="post" action="contact-us.php">