Whats the best way to re fix the edges that are peeling away? thinking to use contact spray adhesive, don't think wallpaper paste will hold?
If it is Anaglypta type paper, then mix up some normal wall paper paste. Use a childs paint brush to get it inside the joints. Wait 5-10 mins for paper to soften and smooth down Patterned Paper, I use a paper glue stick ("Pritt" etc.)
If it is only here and there you can use decorators caulk. After application push into place and remove the excess with a damp sponge/rag.