This is so kind of you to be making quilts for the tiny babies in the NICU.
I worked in hospitals for 30+ years and the NICU used quilts to cover the incubators, to muffle sounds and block light. They loved colorful quilts!
Sometimes when a baby went home, the quilt was gifted to the family.
So I would follow all instructions given. The quilt sizes at my facilities were bigger than you listed, as ours went over "Giraffe" style incubators.
As far as the materials, cotton fabric and either cotton or cotton-poly batting is fine. I preshrink my Warm & Natural using the manufacturer's instructions by placing it into a plastic laundry basket and then dunking that into a bathtub full of hot water. I allow it to soak 15-20 min, then I squeeze it out with my hands as much as possible.
Tumble dry on low-medium heat.
If your batting doesn't have scrim it's going to shred in the dryer, so instead you'll have to let it air dry - I assume you could lay it out on a towel after squeezing moisture out.
When you're all done with your quilt, wash it in warm water using a hypoallergenic baby detergent (unscented).
The NICU nursery will be so delighted to get your quilts!