***Yes they are.***
No they are not. I have killed many an old hen who had perfectly HARD eggs still in them and I used to work in the ggg production industry. I still have a few laying hens for my own use.
http://www.msstate.edu/dept/poultry/avianemb.htm#form
“The shell is added in the uterus or shell gland portion of the oviduct. The shell is composed mainly of calcium carbonate. It takes about 20 hours for the egg shell to form. If the hen lays brown eggs, the brown pigments are added to the shell in the last hours of shell formation.”