Redirect:
use Drupal\Core\Url;
use Symfony\Component\HttpFoundation\RedirectResponse;
$url = Url::fromUri('internal:/');
$response = new RedirectResponse($url->toString());
$response->send();
MessegesMessages using static service:
\Drupal::messenger()->addStatus($message);
Other equivalents:
addMessage()
addError()
addWarning()
References: