I want to use a internationalization option at my jQuery Mobile and jQuery webside. I tried to generate an example with the documentation on http://i18next.com but it seems
Main problem is you can't call i18n.t("menu.surname", { defaultValue: "Name:"}); directly after initialization, as loading the resources from server is async, so basically you try to translate before i18next fetched the resources.
Instead load it with callback:
$(document).ready(function(){
  language_complete = navigator.language.split("-");
  language = (language_complete[0]);
  console.log("Sprache (root): %s", language);
  i18n.init({ lng: language, debug: true }, function() {
      // save to use translation function as resources are fetched
      $(".menu").i18n();
      $("headline").i18n();
  });
});
or use flag to load resources synchron.
By the way:
Your html code has one closing 
The call to $("headline").i18n(); should be $("#headline").i18n();.