Hens have been doing this by instinct ever since there were hens, well before they were even domesticated. Put some trust in your broody, she knows more about what she is doing than any of us.
Will she get out and eat and drink or do i need to bring it and offer her some in the nest?
I agree with Bobbi. The vast majority of hens will leave the nest to eat, drink, and poop with no help from you. I've had a hen get off the nest twice a day and spend over an hour off each time. I've had a hen get off once a day for about fifteen minutes. The majority of time it's rare for me to see them off the nest at all, yet they are getting off because they are not pooping in the nest. They all have good hatches.
Some people like to try to micromanage their broodies, doing all kinds of things to help them, like put food or water in the nest. In my opinion the more you interfere the more likely you are to cause harm.
Should I move her somewhere else so that the other chickens don't bother her?
This is a god question but there is no good answer. We do this all kinds of ways. The risk of moving her is that she might break from being broody. If you decide to move her let us know, we can help you do that to reduce the chances of breaking her broodiness.
I let my hens hatch with the flock. I mark all the eggs I want her to have and check under her once a day after all the others have laid. Sometimes new eggs show up under the broody, it's not unusual for another hen to lay with her. As long as you remove those new eggs each day they are still good to eat. For different reasons you want to remove the extras every day. They won't hatch, they won't go long enough through incubation. If the numbers build up too large that can interfere with the others hatching. So check under her once a day and remove the excess eggs.
If you move her you need a pen she cannot get out of and other chickens cannot get in. It needs to be predator proof or in a predator proof location, like your coop. Inside that pen you will need a nest, food, water, and a little room for her to go poop. You'll probably be cleaning it out often so you need good access.
Bad things can happen either way, you get that when you deal with living animals. Most people are successful either way but you do hear the bad stories.
How long until the eggs hatch?
In theory the eggs should hatch 21 days after you start them. Bobbi told you how to figure that. Theory and life don't always coincide. Even under a broody hen it's not that unusual for a hatch to be early or late, maybe as much as two days either way. So don't be shocked if they are a bit early and be patient if they are a bit late. People have been known to get nervous because of this variation in hatch date. Just don't do anything dramatic if the timing is off a bit. People have ruined hatches by being impatient.
Will my other chickens hurt the chicks once they hatch?
People can get really nervous about this until they get a bit of experience, they read so many horror stories and warnings about this. You are dealing with living animals so about anything can possibly happen but the vast majority of the time the other adults do not pose a threat to the chicks that the broody hen can't handle. If the dominant rooster sees them he will probably figure they are his, even if they are some strange color. Mine sometimes help Mama out with the kids but most just leave them alone.
Most of the other hens pretty much ignore the chicks unless the chicks invade their personal space. Then they might peck the chick. It usually doesn't take long for the chicks to learn to not invade another hen's personal space. Those pecks are usually not that vicious, they are meant to teach the chick to stay away, not to injure it. My broody hens usually ignore when another adult hen does that, but if the hen thinks her babies are being threatened she promptly whips butt. Nobody threatens her babies!
How much room you have is important, broody hens need a little room to work. Perhaps more important is when the broody weans them and leaves them all alone to make their own way with the flock. That's when the extra room can really come in handy.
I have broody hens hatch chicks with the flock and raise them with the flock. One time I had a second broody fight another over the eggs just before they hatched, they destroyed some of the eggs. That's the only time I've ever lost an egg to another adult member. I have never lost a chick to another adult member of the flock. Bad things can possibly happen, especially if your space is tight, but they just don't here.