After you've developed whatever history you can on it, it would be worth a custom frame where it could "breathe" via proper backing and UV glass, etc. with some room so it's not really touching the glass (archival paper spacers, etc.).
You might consider placing a well-written brief history of the piece itself and proudly display it with all its imperfections which are its character.
As to the black and white piece, it looks like a stitch tension example from way, way back when. Might have been from a sewing machine ad/sample, feedsack, etc. In fact, you might find that the small piece has the best history of all.
Whatever you do, protect it until you can display it and then keep it near the settee.
Beautiful. Absolutely exquisite!