I have heard a chirping-like noise when boiling eggs before too. I am guessing it is air being forced through the porous eggshell as temperatures rise. Some speculate the sound is created by the eggs hitting the pan as it boils.
No it's not. When they process eggs they are checked before packaging to be good eggs for cooking, and after packaging they are kept cold which stops the production of the eggs normal life cycle. The only thing that can happen after that is it get rotten, but a chicken will not form in a cold environment.
An egg can have a chick embryo in it. If you put a fertilized egg in an incubator it will grow to a chick. If you eat free range chicken it probably has one in it. The heart starts beating a day or two after fertilization. However commercial eggs are from hens that live in cages and are not exposed to a rooster. You would never hear chirping when you cook an egg Interesting. Egg farmers must "sex" baby chicks when they get them. The male chickens are drowned because they do not lay eggs. A few are raised as fryers but old roosters are tough. I once worked for a chicken farmer
It is possible to find a chick inside an egg especially if you purchased a fertilized one. However, if you want to ascertain that the egg has a chick or not, you can follow or track the development or growth of the chicks inside the eggs by holding up an egg and placing a bright light behind it in order to see inside the egg.
There is always a very small possibility. I watch "How It's Made" and they show how factories package things for supermarkets, make western boots, belts etc. They had one show on crating eggs. It shows how all of the eggs are ran down conveyor belts, the machine separates the eggs, small, medium, large and extra large. The eggs pass under a light which allows the machine to see if it's a fertilized egg or not. The fertilized eggs are thrown out.
Most bird breeders do the almost the same thing with their eggs. I used to breed cockatiels and parakeets. We take each egg, hold it up to a light and you can see if the egg has an embryo in it or not. If not we throw them out so the hen doesn't stop her normal eating or other daily habits by sitting on non-hatching eggs. If some of her eggs are good for hatching then she spends a little less time with less eggs.