Hi Conor and welcome to the forum.
It's certainly an interesting time when you have a broody on eggs - what sort is she? We shall be very interested to hear how she gets on.
Yes, you definitely need to buy some fresh chick crumb, as last year's will be well out of date and this can adversely affect the chicks health and development, which just isn't worth risking. The chicks need the high protein in chick crumb to support their very rapid growth and it will be formulated to provide all they need. The hen will benefit from eating this as well, because she will need building up after her 3 weeks sitting and not eating as much as usual. She won't need layers pellets at first because she won't be laying, but will appreciate treats such as hulled sunflower seeds, mealworms, and green vegetables.
The chicks can stay with her until they are about 6 weeks old, by which time she'll probably be getting fed up with them, and she can go back to the flock if you have any other hens. Then the chicks need to be kept separate from the grown-up hens, and fed on growers food from about 8-10 weeks until about 18-20 weeks, when they too can join the flock and prepare to come into lay. However, this will be quite a late hatch and they may not actually lay until next year, as by the time they are 6 months old, it will be December and light levels will be too low. No problem they will grow on steadily and be good strong birds coming into lay maybe in February.
Where are you keeping her? Do check very carefully that both the coop and the bedding and the hen are free from redmite. There was a sad case on here a few weeks ago where a broody died shortly after hatching her eggs because she was so badly infested with redmite but still kept on sitting nevertheless. She won't want to leave the nest very often, and you may have to lift her off twice a day to make sure she moves her bowels (it will be very big and smelly!) and has something to eat and drink.
Good luck, and keep us posted on her progress!