Yes, remove the PHP code related to those imputs. You should remove:
if ( isset( $_REQUEST['firstname'] ) && !empty( $_REQUEST['firstname'] ) ) { $firstname = $_REQUEST['firstname']; }
if ( isset( $_REQUEST['lastname'] ) && !empty( $_REQUEST['lastname'] ) ) { $lastname = $_REQUEST['lastname']; }
and
if ( $firstname == "" ) { $errors[] = "Enter your fist name in the fist name text box"; $wrong['firstname'] = TRUE; }
if ( $lastname == "" ) { $errors[] = "Enter your last name in the last name text box"; $wrong['lastname'] = TRUE; }
Those lines are on the very beginning of the file.
if ( isset( $_REQUEST['firstname'] ) && !empty( $_REQUEST['firstname'] ) ) { $firstname = $_REQUEST['firstname']; }
if ( isset( $_REQUEST['lastname'] ) && !empty( $_REQUEST['lastname'] ) ) { $lastname = $_REQUEST['lastname']; }
and
if ( $firstname == "" ) { $errors[] = "Enter your fist name in the fist name text box"; $wrong['firstname'] = TRUE; }
if ( $lastname == "" ) { $errors[] = "Enter your last name in the last name text box"; $wrong['lastname'] = TRUE; }
Those lines are on the very beginning of the file.