Contact cement will do the job.
ANS 2 - Epoxy or silicone will also work for this.
Tite Bond 2 will work on cork to cork, but not as well as the new Elmer's Spray Contact glue.
there are sticky pads use those
Silicone will do that.
The new Elmer's Spray Glue is very good for that.
I would use a hot glue gun.
Silicone.
Polyurethane construction adhesive like Sikabond Construction Adhesive will glue cork to marble. You could also use a hot glue gun.
Cork is so porous, I don't think you can get the glue out. It will at least stain the cork. Can you replace the damaged tile?
Cork boards are made by framing a section of cork and glue it to wood or plastic. A cork board is used as bulletin board to post notes and messages.
A spray adhesive would be best for this.
There is no metal that starts off as glue.
contact cement, hot glue, but I would use very small horseshoe nails, or you can make some out of a paper clip by cutting small pieces of it and making them into a U shape, then push them in over the ring and into the cork.