I'm not sure about it slipping through the rings if you did it on the end, but you could certainly trim the tail (along the bottom) with satin or velvet (I don't think velvet would slip on the edges, but it would make sewing thicker at the folds).
I use 45" wide fabric, but you can go as narrow as 36'' imo. I would not go any narrower. I also wouldn't go wider than 45". No need to do anything special for a chubby baby. You can use the same sling for a newborn that you can for a big toddler since they're fully adjustable.