Labelling food products in multiple languages - Can I "automate" or improve the process?

Perhaps I am misunderstanding, but I would avoid ANY process of automatically translating or placing labeling information. The consequences, with both regulatory agencies and customers, could be disastrous.

Packaging is a special field. I can't imagine you have so many products that doing this placement manually, from your pre-translated resources, is a real hurdle worth seeking out an automated or shortcut solution. Just possibly it might be worth using merge or script of some sort if the ingredients change often (perhaps between batches or seasons), but even then, I'd rather keep multiple copies of a label/package on file than edit it often.

Also consider putting the information on layers that can be switched in and out, as needed, or using conditional text.

I'm not sure I fully understand the issue.

I am working with labelling for seafood-products... in a manual, slow way with risk for misspelling.

That makes it sound as though you are manually typing all the text, in all the languages, which would indeed be a tedious and risky approach.

I want to know if there is a way to make a text-box as a MASTER(English), followed by multiple SLAVES(Dutch, French, Italian etc.)-text boxes as seen below... 

I hope there is a way that InDesign can take translations from Excel(or Google Sheet), so for example, when I write in the english textbox:
(MASTER) English: Prawns, Wheat Flour, Salt
... then the following textboxes knows (from my Excel-sheet) that they should say:
(SLAVE) Dutch: Garnalen, tarwebloem, zout
(SLAVE) French: Crevettes, farine de blé, sel
(SLAVE) Italian: Gamberi, farina di frumento, sale

I don't know of anything that would work as you describe there, which seems to suggest you'd want an application that would recognize English words in the 'story' as you type it and then automatically look up other-language equivalents within an external data source and import the translated stories into some associated text frames.

Eric's reply could have something that will work (not quite like that) if you can sort it all out.

The datas from excel are manually translated by our company, since we have a lot of different terms that auto-translations/Google Translate cannot do correct. 

Yes, that rules out any sort of automated machine translation, but it leaves me inclined to ask: If you have the translations already standing in a spreadsheet, what is stopping you from simply placing or pasting those cells in InDesign, negating the tedium and risk?

My couple of cents:

Though it’s possible to base a child master-page on a parent master-page, I’d rather use the following approach: create a layer for, say, English and create labeled text frames for each type of data: e. g. ingredients, recipe name, steps. Then duplicate the layer for each language. With labeled text frames, it’s possible to transfer data by script from an Excel spreadsheet to InDesign: either directly (if you don’t need to keep formatting applied in Excel) or by placing it temporarily on the pasteboard / temporary doc and moving / coping the text. Then you can turn on/off the necessary layers.

There’s no a ‘ready to use’ script that does what you want (but you can find scripts that use this approach) so you have to write it yourself or hire someone.

Yet another approach is XML workflow but I only read a book about it and never used it in practice. Here’s how to prepare an xml file from Excel for placing in InDesign (a short story).

Also, there are a few plug-ins. People on the forum say they are good but I didn’t try them.  

I didn’t mention data merge because Eric already did it.

I would try to use a Data Merge process.

If you document is ready in MS Excel, it is easier to bring the content in your document. 

I would create a 'set of rules' (using actions, styles, GREP,...) to help with the formatting.

This could automate your steps

Merge data to create form letters, envelopes, or mailing labels in Adobe InDesign

Action Recorder for InDesign - Adobe Support Community - 5409538

Take a look here: https://www.id-extras.com/products/translate/