When I modify an untranslated page behaviour (ClassName), the translated pages keep the original behaviour (ClassName) so I end up with un untranslated page ( getTranslation(s) look for the same ClassName ) .
works .... changes in the original language page->ClassName are stored in SiteTree not in SiteTree_Live for translated pages. You need to save & publish every translated page to have changes reflected in SiteTree_Live.
Hm, changing the classname in the original page should update all children... there's even a unit test for this:
http://open.silverstripe.com/browser/modules/sapphire/trunk/tests/model/TranslatableTest.php#l675 (Line 675).
But you're right, the changes aren't automatically published - mainly to avoid accidentally publishing changed content on the translations.