Well if purchasing from a dealer, and they are certified Cessna parts, they will come with the certified EASA STC.
No they won't. If you think that you don't understand the paperwork you should have. The result will be that your next ARC won't be issued if you don't have all the correct paperwork.
If you buy from Cessna, then the parts will come with an 8130 from Cessna. Original parts from the original manufacturer. Simply fit and forget.
Some of these suppliers you quote might be approved under the FAA PMA system. EASA issued guidance on the use of PMA parts years ago but there is still a lot of confusion about using these parts and if you need an STC. For interior plastics, you don't need an STC.
What you might need for a new interior is an EASA approval for a Minor Change. You will need burns certificates (and the FAA certificates are not always accepted by EASA. The FAA don't accept EASA ones). Most of the interior outfits are not approved so cannot work on your aircraft without the supervision of an engineer or Maintenance Organisation.