I have never seen where one hen going broody causes any other hen to go broody. Them going broody is a hormone thing, largely affected by their genetics. Some hens go broody a lot, some only occasionally, and many not at all. There is a lot of discussion on what might cause a hen to go broody but it’s just not consistent. If some of your other hens go broody it will not be because this one did. It will just be coincidence.
Buff Orps and Black Australorps are known to go broody. You might want to build a broody buster to be ready. That’s a raised cage with a wire floor where you lock the broody hen with food and water but no nest of any kind. With the cooler air hitting their undersides they usually break from being broody in three or four days. That cage just might come in handy if you need to isolate a chicken for some other reason. When that happens you often need something like that quickly. It’s good to be prepared.
Letting a broody hen hatch chicks for you and raise them can be a lot of fun. Hens have been doing that for thousands of years, ever since there have been chickens, so it can work. There are lots of different ways you can go about it, leaving them totally with the flock or isolating them for portions of the process. There are advantages and disadvantages to all of them. In my opinion, no one way is right where the others are wrong, it’s just which way you choose.
If you decide to let her hatch with the flock, get all the eggs you want her to hatch, mark them (I use a black Sharpie), and start them all at the same time. Then check under her after the others have laid each day and remove any eggs that don’t belong. There are different reasons to remove extra eggs but if you remove them daily you can still use them without finding any surprises inside.
It sounds like you might be afraid of her. Some can be pretty vicious while protecting their nest, but a lot aren’t. Wearing long sleeves and gloves might make you feel better. When I was a kid my job was to collect the eggs, including any under a broody hen. Most were not bad but a few would really peck hard. But no way was I going to tell my father I was afraid of a chicken. You do what you have to do. I did not have long sleeves or gloves either.
Since I don’t isolate my broody hens I’ll let others talk about that if they wish.
Should you let her hatch some chicks for you? First, my test to see if a hen is truly broody is that she has to spend two consecutive nights on the nest. There have been plenty of times that a hen displayed a lot of signs of being broody but didn’t really fully commit. They quit. But the two consecutive nights test works really well for me.
You never know what you will hatch. I regularly get 2/3 or so of one sex and it can be of either sex. It’s pretty rare that I get a 50-50 split. But the odds are extremely high that you will get some cockerels. What do you plan to do with cockerels?
My last broody hatch last year had seven cockerels and two pullets. Sometimes it is the other way around. You don’t know how many eggs will actually hatch either.
What are the chances your friends eggs are fertile? Probably pretty high. A rooster only has to mate with a hen once every two weeks or so to keep her laying fertile eggs. Some roosters may have trouble keeping 3 or 4 hens fertile but many can easily keep over 20 hens fertile. You can always crack a few eggs and look for the bull’s eye. If the ones you crack are fertile, the ones you don’t crack should also be. This link has photos of what to look for.
Fertile Egg Photos
Eggs can easily be stored for over a week and still be hatchable. In good conditions they can be stored over two weeks. Just don’t keep them in high temperatures like over 80 degrees of cool temperatures like in the refrigerator. People do hatch plenty of eggs kept in these higher or lower temperatures but your odds are better if you can keep them somewhere in the middle. The “ideal” temperature to store them is around 55 degrees but I keep mine at room temperature, usually in the 70’s, and they do fine. You don’t have to be in a rush to get them under the broody, but sooner is usually better than later.
I know it can be stressful, especially the first time when you don’t know what is going on. But try to relax and let the hen do her job. A broody knows what to do a lot better than we do.