I’ve seen a broody hen get chicks down from a ten feet high hay loft. Mama said jump and they did, then bounced up and ran to her. My suggestion is to leave her alone and let her decide when they need to come off the nest. If you do decide to move them, be careful. Chicks like to crawl up under the hen’s wings and in the feathers. I crushed a chick once when picking up a broody hen. The more I interfere the more damage I generally cause. I don’t interfere much with a broody any more.
One danger with waterers is that the chicks can get in them and not be able to get out so they drown. I suggest you fill the waterers with rocks or something (some people use marbles but rocks are free here) so the chicks can walk on top of the water.
You do need water where the chicks can get to it. I don’t know what kind of waterers you have or how they are set up so it’s hard to get too specific with suggestions. In my brooder I use this. I have set this up on a paver where the chicks can get to it when they are raised with the flock, but now I use something different.
I make a platform around a dog bowl (black rubber in winter or inside the coop so it can be emptied if it freezes, white plastic in summer in the sun so it stays cooler) and fill the bowl with rocks when I have young chicks. They can hop up better than most people think. In the coop I spread a piece of plywood on top of the bedding and place this in the middle to help reduce the shavings being scratched in the water.
Many people isolate the broody hen and chicks when they eggs hatch. Some totally isolate them until the chicks are practically grown. Many isolate them for a day or two to help them get more mobile, then let them loose with the flock. Mama will protect them if they need it. Usually mine don’t need much protection but occasionally Mama whips butt if any chick threatens her babies.
I generally just let Mama bring them off the nest whenever she decides to and let her raise them with the flock. There is no specific right way or wrong way to do any of this, mainly just the way we choose. It’s possible there is something about your flock or your set-up that indicates one way might be better than another. If your space is tight it can be harder for Mama to raise them with the flock. But if your space is that tight you will probably have trouble integrating them later anyway. The biggest risk to the chicks if your space is tight is not when Mama is raising them but after she weans them and leaves them on their own with the flock. I’ve had a couple of hens wean their chicks at three weeks in warm weather and those chicks were fine with the flock, but I’ve got a lot of room. Most broodies wean them between 4 to 9 weeks of age.
After a chick internal pips the chick still in the egg starts talking to the hen. The hen knows when more are coming. I’ve had hens bring their chicks off the nest within 24 hours of the first chick hatching, I’ve had some wait more than three full days. I usually open the unhatched eggs to see at what stage they stopped developing. I’ve never had a hen leave a live chick behind. But mine are always started at the same time, I mark the ones I want her to hatch and check daily to remove any others. I think yours were all started at the same time, I hope so. I think you have the best chance of getting the most chicks to hatch by letting the hen decide when to bring her chicks off the nest. If I don’t interfere I am less likely to cause harm.