I found two more troubles, trying to get a multi language store running.
1) The links to the cart/checkout page always send me to the English (standard) version of the cart/checkout. Also going from Cart to Checkout gets me to the English version, even when I’m using the translated version of the page. And even though the cart and checkout pages are translated, the mouse-over version on the frontpage never translates.
2) The settings are set that the billing address is the default shipping address, but when I change the checkout page to the other language, all of a sudden the fields for the shipping address show up.