Oh my, that requires a long reply. i'll try for the short reply:
She should not stay in the nest box. Other chickens might try to get on the eggs and break them if they fight. I have had this happen more than once. I think other hens find a nest with eggs attractive. Also, if she comes out to eat, she might go to the wrong box and the eggs will die. I've had this happen also.
She needs her own broody place, with food and water available nearby. It's kinda late for a broody (although I have three right now). You might check to see that she is really broody and not just ill. She should be mostly bare on her breast feathers, and should puff up and holler at you some when you stick your hand in there. She will also go right back to the nest after you take her out. She might sit on the ground for a few minutes, but will go back in. If she hasn't been out for a while, take her out. She will probably walk around and poo.
