You should probably move mom and her eggs to a cage by herself either now, or when the eggs start to hatch. You should keep the chicks and adult chickens(except the mom) apart for as long as you can and slowly introduce them by leaving them in a cage in the coop for a couple before letting them...
Try checking her for parasites, you can do this by picking her up parting her feathers around her preen gland, vent, under the wings, etc, and look for tiny bugs running away from the light. You can also look for eggs along the feather shafts. If she doesn't have bugs she could be sick and you...
I've always fed them the same food and never had a problem, but if you're worried you can feed them calcium out of a separate feeder or scatter it in the ground in their run.
RIR are good for eggs but they tend to burn out after a couple of years and stop laying. As for friendliness, they can either be super sweet and docile or nasty and beat each other up. If you're okay with having them shipped you can check Cackle Hatchery or Murray McMurray Hatchery.
You can scatter grit and oyster shells in the run or you can offer it in buckets, the chickens that don't need it don't normally eat it, so you shouldn't go through it too quickly unless they scrape it out of the bucket and scatter it on the ground (which they might do).