BuddyPress.org

Hi,
I am working on the login form on the home page and I use “WordPress Login Form”. To avoid being redirected to login.php after entering the wrong data and when the form fields are empty, I pasted the following code. I have a question, how do I add a login error message to a custom login page „WordPress Login Form”?
ps. I think the added code does not have to be divided into two parts. Can it be shortened?

<?php
//Is the data correct
function my_front_end_login_fail( $username ) {
   $referrer = $_SERVER['HTTP_REFERER'];  // where did the post submission come from?
   // if there's a valid referrer, and it's not the default log-in screen
   if ( !empty($referrer) && !strstr($referrer,'wp-login') && !strstr($referrer,'wp-admin') ) {
      wp_redirect( $referrer . '?login=failed' );  // let's append some information (login=failed) to the URL for the theme to use
	  add_action( 'wp_login_failed', 'wp_login_form');
      exit;
   }
}

//if the fields in the form are empty
add_action( 'wp_authenticate', '_catch_empty_user', 1, 2 );
function _catch_empty_user( $username, $pwd ) {
	$referrer = $_SERVER['HTTP_REFERER'];
  if ( empty( $username ) || empty( $pwd )) {
	  wp_redirect( $referrer . '?login=failed' );
    exit();
  }
}

?>