The answer for redirect a user that fails log in is here: https://www.wpinsite.com/code-snippets/how-to-redirect-wordpress-failed-logins/
Add this to your functions.php:
add_action( 'wp_login_failed', 'my_front_end_login_fail' ); // hook failed login
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
exit;
}
}
and it works like a charm. This code redirects to the same page as the user tries to log in from. Change $referrer for another page.