Cayuga duckling missing feathers
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I've raised two batches of cayuga ducklings and i've never experienced either of those issues. The dry eye makes me wonder if she is somehow dehydrated. THe missing feathers make me wonder if she was being picked on by her pen mates at TSC or if she somehow got a mite infection from the poultry area.
I am not an experienced duck keeper. I'm only commenting that the ducklings appearance is outside of my normal experience.
Perhaps a more experienced duck keeper can provide advice.
Were there bigger ducklings, geese, or chicks in with this duckling at TSC? She really looks like someone who has been picked on and had her eye injured and back fluff pulled out. That eye looks pretty bad, I would really suggest a vet if you are able to take her to one. In the meantime, you can make up a saline solution (you can look up online how to make it, very easy) and flush out that eye really good several times a day. That might help, but it really does look injured and may need some stronger eye drops or eye gel medication.