One thing I would suggest is that if you use reproduction fabrics--make sure you wash and dry them so that any shrinking they are going to do will be done before it is added to the quilt. Personally, and I think I may have seen this somewhere, I would put a replacement piece right over what is there. I would mark the quilting pattern, that is already on the piece you are replacing, on a piece of tracing paper. Then I would applique the new piece on and use the tracing paper as the guide for how to do the quilting over. Like Margo said, I would try to match the thread that was used (probably cotton) to replaced any quilting.
The 1"x2" area is a whole different problem. Is it where a flower was? If so, I would trim out the excess and trying to match the backing, replace it all by hand. The only way I would use wonder under for the frayed areas is if I wasn't planning on replacing them. Since you are only going to use it for display purposes, it would hold but it will also cause that part of the quilt to be tight against the batting and I am not sure that is the look I would want. A lot of this is really up to you. Just went back to reread what you wrote and you said you would be using a one sided fusible so I guess that would not be a problem. I am not an expert--these are just my thoughts on how I would tackle it.