Do you have the hens already and they are broody, or are they currently broody at where you're getting them from. I only ask this because a move to a new coop could potentially break their broodiness.
Barring that possibility, here's my experience:
Just put the eggs under them as they sit. When I have a hen that has begun sitting off and on I test her by putting an egg next to her, if she's broody she will tuck it under her and then literally puddle down over it, spreading her body out as far as possible. Broodies also pluck some of their feathers to create a 'brood spot' where they can put the eggs right next to their skin for incubation. If you pick a broody up you'll notice a featherless spot on her underside.
You can take the chicks away and put them in a brooder. Personally, I let the hen raise them, it is soooo much easier.
I wouldn't let a hen sit for more than a hatch cycle. Although most do eat/drink, they become very deconditioned and its not unheard of for them to die on the nest.
How many eggs, as many as can fit under her and stay warm. Hen's can usually handle 12-15 of their own size eggs, or an equivalent mass of smaller/larger eggs. Keep in mind that the more you put under her, the more likely there will be a broken or unincubated egg.
You can easily keep a hatching egg for a week or so at room temperature. Just make sure they aren't exposed to temperature extremes.Remember, hens lay a clutch over a period of a couple weeks before they even sit to incubate.
I'm sure others may have other opinions & experiences.
Good luck & I hope this helps.