I did more tests. Now I have made the following settings:
It is important that you use the same alias in the German and English menu items, in this case "shop". I didn't know that you could use the same alias multiple times (probably only because there are different language menus) .
Then the checkout button works correctly:
/de/shop/cart-cart (German menu)
/en/shop/cart-cart (English menu)
Furthermore, these two menu items must not be linked.
