Pecking feathered feet is normal, because feathered feet are not normal. It's a human creation that goes against what chickens know about chickens. Especially if the broody does not have feathered feet herself. Chickens peck things that look out of place. Deep shavings help with that, if the feet sink into them and the feathers are harder to see.
Broodies continue sitting on the chicks for a couple of days post hatch, when they are still very young and weak and get cold easily. With store-bought chicks, they are older when the hen receives them than they would be when she hatched them, so in her mind they are newborn and still need to be sat on. If they are a couple of days old by then, they'll want to get out and explore, and she might try to peck them to get them to go back under. You don't need to take them out to feed them. At some point they'll get strong and rowdy enough to get out and go explore anyway, and she won't be able to control them so tightly anymore.
Broodies continue sitting on the chicks for a couple of days post hatch, when they are still very young and weak and get cold easily. With store-bought chicks, they are older when the hen receives them than they would be when she hatched them, so in her mind they are newborn and still need to be sat on. If they are a couple of days old by then, they'll want to get out and explore, and she might try to peck them to get them to go back under. You don't need to take them out to feed them. At some point they'll get strong and rowdy enough to get out and go explore anyway, and she won't be able to control them so tightly anymore.