Normal lining shed is pink and stringy. Blood is watery and darker red.
I'm not seeing "blood" in the photos, unless I am simply missing something. I see normal pink lining.
And layer feed is fine for chickens. It is what they should eat. They should also get plenty of room to scratch and forage, but mine eat good quality layer predominately.
Corn is like candy, and should be used sparingly.
You've also moved them which produces some stress, which generally will bring on shed lining.
Since you've got no close vets who treat chickens, you could as a matter of course worm them and treat them with Corid.
You can find Wazine or Safeguard and Corid at your local feed store. If need be, you can mail order it from Amazon or Jeffers Pet.
I personally isolate newly acquired adult birds and place them on medicated chick start to allow their guts time to acclimate to the coccidia in my soil. I watch their droppings carefully for 2 weeks. If there is no sign of rank blood, I remain on the Amprolium based medicated for another 2 weeks, then integrate. If I see rank blood, I begin Corid (higher concentration of Amprolium).
Also look them over for potential external parasites. It is no fun to have to treat the whole flock if your newly acquired birds bring in mites/lice. I also thoroughly dust any newly acquired adult bird in isolation time.
I'll link a poo chart so you can see the differences. Only you can tell what you are looking at as photos can be misleading.
http://www.the-chicken-chick.com/2012/02/whats-scoop-on-chicken-poop-digestive.html
and this one
http://www.fresheggsdaily.com/2016/03/all-about-chicken-poop-brown-black-and.html