Hens have been going broody and hatching chicks on their own without human intervention since before they were first domesticated. They did not go extinct. We've domesticated them but many still have those instincts.
I've had broody hens come off of the nest twice a day for over one hour each time. I've had a hen come off every morning for 15 minutes. I've had many that I never saw off of the nest but I knew they were coming off because they did not poop in their nests.
Is it possible one could starve herself to death or die of thirst? You are dealing with living animals so anything is possible but I've never had one do that.
A hen's comb and wattles should be bright red when she is laying eggs. That is a signal for the rooster that her eggs need to be fertilized. When she is not laying, like when she is broody, the comb and wattles pale so the rooster will leave her alone.
Hens store up a lot of excess fat. That fat is mostly what they live off of when broody. That way they can stay on the nest and take care of the eggs instead of needing to go look for food and water. They are using up that fat so they are losing weight. It does not mean they are unhealthy, it's just fat put there for that purpose.
I doubt that anything I can say will make you less stressful. Maybe after you've seen a few cycles. I grew up on a farm where the chickens free ranged and raised chicks so I grew up knowing that they can manage. All we did was mark the eggs and remove any that were laid in the nest and did not belong. The hens did everything else.
Cochin are known to go broody a lot. That does not mean that every cochin will go broody often, but many will. It's bred into them. The only thing you can do is break her from being broody if you do not want her to hatch eggs or raise chicks. Or get rid of her and get breeds known to not go broody often. That does not mean you will never have a broody but the occurrence should be a lot less.
