Real or Fake  

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Despite the unnaturally red-tinted finish on the otherwise rather bland wood panels, the set looks legit to me.

For me it is fake 

@julierigaut

There are a lot of tutorials on the web how to recognize the authenticity.
Methods of verifying are for example measuring the thickness of the plywood (8 mm). Or what about the cushions, usually they are removable, if not, it's a replica. For more details, just watch the tutorials.

For me, it looks pretty real. But is it used? If yes, then for how long?

Cherry was used in the 1990s by both Herman Miller & Vitra.  This is from a late 1990s catalog of the short-lived retailer Full Upright Position (Portland, OR)

Do you think people would really go as far as sticking a fake Vitra label ?

Vitra Eames Lounge chair in Cherry.

Here is someone disassembling an original chair: 

https://youtu.be/ROdcdaD7cnc