if snow is what she needs I can send you some

I have a foot already, and I am not afraid of running out. She looks beautiful (both transparent and in color). The egg shape is just pattern recognition. Human brains see things like faces in landscapes, so seeing egg shapes in the shadows of a chicken x-ray is easy, no worries. Let the vet tell you if it is really there. Watery-poops is likely just her drinking because she has unfettered access. No one to fight her for the water dish! I see it a lot when I give wet mash instead of the dry foods. Water in-water out. White in poo is just pee, and mucus comes out of all our intestines. She may just be a little fragile in eating always, she was a fragile baby, she just isn't a big eater. Is the vet ok with her weight ? It looks like good news
Except, I think you now have a house-chicken (like a house-cat), she isn't going to want to fight the others for the dish anymore. Do you want to keep her inside ? My husband would not let me, I would keep ALL of them inside if I could. He says I would sleep in the henhouse if he let me. (probably true, I get up at night to check on them sometimes, if I could put a bed out there it would be simpler)
(assuming she has to go back to the henhouse) I think I would just give her a little sleeping cage in the hen house with her own bowls to eat & drink so she doesn't have to fight for it, she can snack in the morning and in the evening. I have some chickens that don't get access to the bowls when I set them down, so I make sure there is food at night, they get up when the others are sleeping and eat a little. I have one so far on the hierarchy that she naps with the eggs during the day and eats at night. She stays a little later inside the coop on cold days. Not her fault her sisters are bullies! (I commiserate, because my sisters are bullies too, so maybe I am extra sensitive to it.)
I think Heni is doing great

I hope you are too.