Does it have an unusual or weird smell? Do you have badgers where you are? It could be badger, raccoon, opossum, cat or dog based on the appearance of the scat, and with no additional information. If you find another one break it open to see if it includes bones or fur, and note it it has a...
We have a secure run and coop like yours with the hardware cloth skirt. We leave the chicken door open in the summer and close it for storms and when it's cold or snowing. We have never had a predator get into our run or coop.
I open my incubator to remove dried chicks or egg shells, and have yet to have a shrink wrapped chick. However, my house is 65-70+ humidity so that probably influences it.
I don't know if they can, but I had an enthusiastic chick standing on one's head literally at the moment it hatched and I decided to put the dry one in the brooder. I usually give single chicks a sock full of dry rice or just a sock to snuggle on. Your incubator has lots of room for them to...