Sick chicken with creamy yellow poop with a orange looking thing in the center

[Lil Brown Nugget]

Unfortunately that looks like a lash egg, and that means she has salpingitis, which is inflammation of the oviduct. Sadly it can't really be treated, and all you can do is offer supportive care measures.
Her not laying and having a messy bottom is another sign that she has salpingitis.

What causes that? Is it contagious? How long do they live after catching the infection?

 

[Eggcessive]

Salpingitis is very common in hens. Bacteria can enter the oviduct via the bloodstream or it can travel up the oviduct from the vent, and cause inflammation and infection. Internal laying and lash eggs can occur. They may have it for a few years, and many hens who are processed for meat may be condemned because of it. It can lead to coelomitis or egg yolk peritonitis. Here is some reading:
https://the-chicken-chick.com/causes-of-lash-eggs-salpingitis-by/

 

[Lil Brown Nugget]

Salpingitis is very common in hens. Bacteria can enter the oviduct via the bloodstream or it can travel up the oviduct from the vent, and cause inflammation and infection. Internal laying and lash eggs can occur. They may have it for a few years, and many hens who are processed for meat may be condemned because of it. It can lead to coelomitis or egg yolk peritonitis. Here is some reading:
https://the-chicken-chick.com/causes-of-lash-eggs-salpingitis-by/

Thank you for the link. Today gathering eggs I noticed one of the two Easter eggers layed an egg that looks odd. So I hope it’s not going around the flock. I still have the compine separate.

 

[Lil Brown Nugget]

This is the hen that is sick. I was told she was a Silverlace.

 

[Tookie]

Thank you for the link. Today gathering eggs I noticed one of the two Easter eggers layed an egg that looks odd. So I hope it’s not going around the flock. I still have the compine separate.

I don't see anything alarming with that egg. Just uneven pigment or calcium deposits.
I could be wrong, but I don't think salpingitis can spread?

 

[Tookie]

This is the hen that is sick. I was told she was a Silverlace.

Aw, poor girl. She's a pretty little hen.