How to send “Location” header on plugin form submit event?

You’re trying to send a redirect header on the admin_menu action, which is fired after some of the page has been sent to the browser. You have to hook an earlier action before output starts, like init.

add_action( 'init', 'wpa_test' );
function wpa_test() {
    if(isset($_POST['submit'])) {
        wp_redirect( home_url() );
        exit;
    }
}