It is because the running is caused by the nerves endings. This happens when the brain is suddenly disconnected from the rest of the body.
There is none. A 'zygote' is the scientific term given to a fertilised egg.
At the point when the first chick hatches most hens will get up off the nest to clean up and remove shell pieces. Like cleaning house. They usually also eat/drink and defecate away from the nest. They return quickly though to continue hatching the rest of the eggs and offer protection to the emerging chicks.
Meat is usually defined as the flesh of an animal, so eggs are not meat. It's certainly an animal product, so no vegan would be consuming it. Some vegetarians may eat it, some may not.
Eggs Are Not MeatAn egg is a dairy product, not a meat.