The eggs you put under them make no difference, as long as they are fertile. Some grocery stores carry fertile eggs too, such as Trader Joes. I understand the hatch rates aren't the best though, 1 or 2 chicks out of 12 eggs.
How each hen does in the flock with babies is an individual thing. Some do well and raise their babies with no problems, others do not protect them well and it ends up in babies getting crushed. I usually move mine after the chicks hatch to private quarters that are still visible to the rest of the flock. I have had broodies freak out if you move them when they are sitting. But once the babies hatch, you can move them at night to an area of the coop that is a bit more private. If you keep them within sight of the flock, they will not have any trouble rejoining the flock. I keep mine separated for a week, then let momma and babies out with the flock. It works very well and I had 10 broodies last year.