Hi Giuliano,
Sorry for the late reply and thank you for your interest in langify!
Yes, I can confirm that your customers will see the checkout page in their currently selected language if the translations are available and if you are using the new Responsive Checkout.
You can translate your checkout page in langify or in shopify itself (the latter one should be preferred).
Luckily shopify already comes with the translations for the languages that you've mentioned so that you won't have to translate your checkout page at all unless you want to change some of the already available translations :)
Best Regards