For your quilt, i would just replace the binding, either by removing the old one and putting a new one on, or just put a new one on over the old one. For the quilting, just redo it where it is needed. Would love to see a photo of your special quilt.
Sounds like your friend's quilt needs more work. Probably a new backing is in order, remove binding, place new backing on and rebind. I would not would just tack or tie the new backing and not worry about totally requilting it. Guess it depends on what it looks like.