Your quilt is so pretty and I think the name is just perfect. I have done labels a couple of ways. I have hand embroidered them, my machine has basic block letters and I have used those and I also have written them with a pigma pen.
I am not getting how you are going to use the basket block. Is your intention to applique it to the front of the quilt? If so then do you currently see through the background fab when you place it on the quilt? If this bothers you then I would suggest putting a foundation on the back. This will make it easy to applique as well because you can stitch the backing on the block inside out and leave an open space to turn it right side out and when you applique it on your seam allowance will already be turned under from sewing on the backing. For quilting, you may wish to put flannel inside for a lightweight batting. I've never done a quilt with no batting so can't say for sure. For quilting, your top is so pretty and I am sure Mary will love it so no need to get too fancy but I would put enough quilting in to make sure it is enforced. You could do a simple diaganal grid or do SID. Or if you are feeling brave FMQ an all over meander or stylized flowers on it. I am sure she will love and cherish it no matter what you do.