First eggs... what is this?

Hens systems often need to work out the kinks when they first start laying. She may have released another yolk that shot thru and covered your egg in gunk. Just keep an eye but they should work it out. As for pecking it's a curiosity thing. Place golf balls or fake eggs in each nesting box so they can peck at them and become bored when nothing happens. Ideally do that before they start laying on their own. Good luck

 

Are these new layers?
Yellow gunk is yolk from another maybe soft/thin shelled egg.
Shells appear to be thin and will be broken(and eaten) when pecked for curiosity.

What and how exactly are you feeding?