How do broody hens build their clutches without their first eggs dying?

First off, I'm new to hatching eggs. I bought this Black Star hen 6 days ago from a lady. When I picked her up, she had a nest of 3 somewhat warm eggs in the stall that she was kept in, which I put into the fridge at home, and thought nothing more of. Now I'm beginning to wonder if she is broody. She has, ever since the beginning, built up a big nest in the corner on the ground of our chicken house. There are 10 other hens with her. She would lay and I would go take the egg, she wouldn't growl or puff up, but raise her tail up and down weirdly and wouldn't move, I'd have to set her aside. I kept taking the egg every day, not sure what was going on with her, but yesterday she refused to leave and go out into the run after I took her egg, even when I threw out treats and the others were spazzing out over them. I decided today to let her keep her egg, and she barely keeps it warm, and doesn't stay on it constantly like I hear about. She is only on it long enough to keep it warm and then either stands beside the nest or goes into the run for a few minutes and comes back to stand next to it again. She moves it around some and covers it in straw. What is she doing? Is she broody or just being weird? At least 1 of the 3 eggs from her clutch at her previous owner's had a big vein going through it, so I threw it out when cooking. Not positive, but wouldn't only a broody hen stay with an egg long enough to get it to actually start growing? If she is broody, does she barely keep it alive for the # of days she builds up her clutch, then finally actually sit on them to incubate them? Sorry for all the questions, I'm sure I've actually forgotten some LOL.