Hi,
The setting "Translation published by default" is only visible when deactivated. Once you activate it, it is removed. And when you install a new HikaShop, it is activated by default.
So if you see it, it means that you had it deactivated with an old version of HikaShop and then updated.
We did it like that so that the behavior didn't change for people updating, but that for people installing HikaShop the setting would be always activated. That's because it lead to unnecessary support as you usually want it to be activated.
In any case, that setitng is not linked with the display of the translation file translations on the frontend.
If you don't get all or part of the translations from the translation file on the frontend it means that you have syntax errors in the translation file.
Turn on the debug language setting of the Joomla configuration, and at the bottom of the page where you don't have the translations working, it will display the debug data telling you on which line of which file are the problems so you'll be able to easily find them.