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
Yes, they're just starting to lay. Eggs though pecked, we're intact. No other eggs or she'll anywhere, doubtful one was eaten. Shell was a little thin, but still tough upon breaking it open. They have layer available at all times and are free range.