welcome to the board!! how nice of you to make a quilt for this lady.
Can you test to see if the quilting lines will disappear? usually there is some branding "bucilla" or whatever along the edge, in the same stuff as the markings. Wet it with a washcloth, rub and see if it comes out. I have done these kinds of tops and the marks never came out.
Maybe steam it to get it to relax? hang in the bathroom after a hot shower?
There are some nice thin battings, Warm & Natural comes to mind. Get 1.5 yards of backing if it is really 45" wide with NO selvages (is there any such animal?) - otherwise I would piece the back or get some 60" wide, 1.5 yards.
Hope you can find someone to help you finish it.