One thing you need to remember is that not all hens/breeds get broody. The number of eggs she lays really depends on the hen. I had 2 that layed eggs for a month straight before going broody, and 2 that lay 6-7 eggs before going broody.
The eggs do not start developing until the hen sets on them. No matter how many eggs she has, if they were put under her at the same time, they should hatch within 24 hours of each other. The hens will usually leave the nest when the chicks are 1-2 days old, in my experience, leaving any remaining eggs to die.
I would recommend putting a broody in her own pen or cage, just so the other hens don't lay eggs with her. They could potentially fight, causing the eggs to break as well. Also, when the chicks hatch, the bigger chickens might peck at them, or the mama could be very protective, and it is just a very stressful environment for all parties. Too much stress is not good, especially if you are raising them for eggs as well. This could cause the others to stop laying. You do not have to let the hen go broody, just keep taking the eggs away, and eventually she will stop.