There are no easy answers to your questions. Answers depend on the situation. If the mare is a maiden mare, she needs more time to bond with her foal then an experienced mare. Some mares are very protective of their foals and it may be unsafe to enter the stall unless you absolutely need to enter and are an experienced horse person. If every thing is normal about the birth process, there is no need to enter the stall until the foal is up and potentially has nursed. Foals should be up and nursing within 2 to 3 hours of birth. As to how long a foal should remain in the stall, foals don't need to be born in stalls. A great place for birth is a nice green pasture, but it is hard for people to watch mares for problems during birth when they are out at pasture. Once the foal is up and nursing, the stall can be cleaned. The placenta should be removed as soon as it is passed and examined to make sure it is complete. Foals can be turned out if the turn out area is safe and the weather permits within a couple of hours of standing and nursing.   As for eating hay and other feed, the foal will try to mimic what the mare is doing when she is eating within the first few days, but will not really start to consume feed until it is about 2 weeks of age. The speed of feed consumption also depends on how much milk the mare is producing. If the foal is hungry, the foal will eat dry feed much quicker than a foal from a mare that is milking well.

Anytime the situation is not normal during the foaling process, the mare and foal (if born already) need to be checked. Once your book is written, I would have someone experienced with foaling mares read the areas for accuracy.