I had this problem. It is my understanding that soft eggs are the result of two thing: not enough calcium and/or Vitamin D in the diet. Put out oyster shells for the calcium and add Poly-Vi-Sol without iron (baby vitamins sold at the drugstore) to their water. I haven't seen any dosage instructions for the Poly-vi-sol, so I add 1 dropperful/gallon of water and it has been working fine.
Re: the egg eating. Realize that eggs attract predators. When an egg breaks the chickens go nuts eating it and it occurred to me that they probably developed a taste for their own eggs as a protection mechanism.
I hope this helps. I'm fairly new at this myself.