Ive heard of using kelp as a supplement. Its supposed to be pretty awesome, but its kind of expensive and my hens are great without it.

Egg shells are a fantastic source of minerals! Hens use up a lot of minerals creating eggs, and generally need a source of calcium. Some people use oyster shell, but I find they get enough between the eggshells and free ranging, that I havent had to purchase anything else.
Ive never had issues with egg pecking. I think that really stems from being confined too much and they are bored, and possibly fighting over nests and breaking an egg accidentally. They will clean up an egg that was stepped on and broken by mistake. I even had a neighbor give us a hen for the stew pot because she was a notorious egg-eater. She came from a very small coop. I decided to give her a chance, and it turns out she is quite a good egg-layer, and has not eaten a single egg while here. She is still runniing around outside, actually.

The pan scrapings and leftovers are whatever we have, so no, not vegetarian. They can eat pretty much anything. They are omnivores and while free ranging eat grass and grain, as well as insects and small animals. I have seen them catch and eat lizards and snakes. So I don't feel the slightest bit bad about feeding them leftover meat scraps or anything else. And yes, that includes chicken scraps. They do not care. :)