Usually a broody gets off the nest once a day to eat, drink, poop, and maybe ge t a little exercise or dust bath. If you're not finding poop in the nest, she probably is. If you have other hens, one of them could be moving the egg. Sometimes another hen will lay her egg in the broody's nest, either while she is gone or right on top of her. Sometimes other hens will move eggs out of or into the nest. And sometimes a broody will remove an egg herself; this could be because she senses the egg is bad.
Many people let their broodies set and hatch right i with the flock, as chickens have always done, and others prefer to separate them into their own little area for the setting. If you leave the broody with the flock, its a good idea to mark the eggs with a Sharpie so you know which is which. After the eggs hatch, you can al do it either way. I prefer to let my broody set in a separate room, then raise her chicks in with the flock (they will want to join the flock at a day or two of age.) If you do this, feed the whole flock the chick feed as layer feed will harm them, and chick feed will be fine for the adults for a few weeks, even if medicated with amprolium. The broody usually gives up her motherly ways around 4 to 6 weeks, goes back to roosting, and resumes laying eggs. If the chicks grow up with their mama in the flock, she should protect them from any bothersome hens, and by the time she is through mothering, they should be an accepted part of the flock.
Here are a few links in case you want to read further. There are many threads on here about people's experience with broodies -- and many ways to manage them. Good luck!
https://www.backyardchickens.com/a/guide-to-letting-broody-hens-hatch-and-raise-chicks (post 5)
http://www.themodernhomestead.us/article/Broody-Hens-1.html
https://www.backyardchickens.com/t/693407/broody-bird-what-to-do/0_20#post_9400530