Hi,
Falang's translation mechanism works only on the frontend of the website.
So if the emails are sent by an action you do on the backend, like changing the status of the order, Falang won't kick in and thus the text won't be translated.
For the product names in the email, the name itself is stored with the order when the order is being created and used "as is" in the email so there is no translation ocurring and that's why it works fine.
But the shipping/payment method name is dynamically loaded when the email is generated, and that's why you only have the issue with it.
The solution is to not do the translation of these with Falang. Instead, create a new translation override under the Languages tab of the HikaShop configuration.
For example:
MY_SHIPPING_METHOD="shipping method name"
Then, change the name of the shipping method to MY_SHIPPING_METHOD in the menu System>Shipping methods.
That way, the translation mechanism of Joomla will automatically use your translation override for the current language (like the rest of the email content) and it will work on both the backend and the frontend.