Love that name
@buffy-the-eggpile-layer !
If I may interject my unprofessional opinion.
I don't think the egg eating is more bullying, rather, just food in the coop that the others eat. Which is a good sign, at least the eggs are edible!
In the OP, you have physical and mental health at different levels of concern, I believe they are closer linked, mental health directly effecting physical health, and vice versa. Seeing it this way may hepp you solve the problem.
That said, if you remedy any one of her problems, it sounds like she'll have what it takes to rebound.
Fortunately/Unfortunately....
Seems the bit of isolation necessary to fix one problem will also fix them all!
Best!
Sorce