Yes, almost every single broody I've had has moved spots after some of the chicks have hatched. I'm not sure if it's because the chicks started moving around and she tried to cover them or something else.
I didn't realize in your original post that she already had a chick hatch. When my broodies hatch they've always moved a little away from the original nest site.
A regular flashlight or phone light will work. Just shine it through the fat end of the egg. Not sure why she moved her nest but at least she is still sitting on the eggs. What day did she start sitting?