Do I use Twig filters 'include' and 'extends' for localized site correctly?
From the localization guide - When Craft is looking for a template, it first sees if a template with that path exists inside a directory named after the current locale, then for the actual path provided.

So in your case, when you're in the de locale, it would look for the following templates:


templates/de/_layouts/base.twig
templates/_layouts/base.twig


and


templates/de/_includes/header.twig
templates/_includes/header.twig


etc, using the first one that exists.

If there's little or no difference between how the site behaves in different locales (other than the translated strings,) then it might not be necessary to override whole templates like that, but it's great when you need it.