Speaking as a textile restorer/conservator and commenting under the impression that this quilt will not be used: please don't cut, use fusible anything or machine quilt with fancy stitching. Just cover the hole with netting and darn, then cover with a patch of cotton and turn under the edges and hand stitch with very fine silk or cotton and using a very, very fine needle.
Remember to tell your friend that, over the years, the patch will fade at a different rate and colour than the rest of the quilt.
As for the binding - if you go over the old, secure any lose edges and attach the new binding to the quilt by hand because years from now if the quilt requires further work, it will be easier for the restorer/conservator to remove it and hand stitching is kinder than machine stitching.