This is how big it is. She lives in the coop inside the coop which was once theirs. The nearing boxes are in there I would have never swarmed it would have taken this long
How big is your coop and run, and what breeds do you have? Do you have enough room for everyone? Has this new one been living in a cage for the last two months? Ideally, to integrate a new bird, you put them in a pen right next to the flock. This way, they get to know each other without hurting each other. Keeping the new girl in a cage inside the run doesn't allow the established flock to sort out pecking order, and it doesn't allow the new girl to behave in a normal manner. As for space, a medium sized breed (i.e. Leghorn, Hamburg) needs 4 sq ft of coop space, not including roosting space and nest boxes; and 10 sq ft of run space. If your coop is in the middle of the run, then you need to subtract the coop sq footage from the run's total. Larger breeds like Orpingtons and Rocks need even more space.
As for the egg eating, it's usually caused by not enough protein in the diet. Increasing the protein intake and reducing the amount of goodies being given will help. Do they have access to nest boxes? If they have recently been moved to a new coop, they may not be laying at all.