An egg whose shell has been cracked is no longer fresh. It is subject to bacteria. These days, we know that even whole eggs may carry Salmonella. Do not eat raw eggs. They do come in sizes.
Large eggs are best in most recipes.
Whole egg substitutes can be used in most recipes. A sponge cake is a very delicate cake with a smooth, even texture. It is made light by eggs and beating. A butter cake is made rich by the use of shortening and light by eggs and some baking powder. A butter cake with the addition of flour becomes a loaf cake.