How long has it been like this?
Distortions of the neck can be the result of many different problems. Nutritional, viral, bacterial, injury and genetics. Oftentimes providing supportive care, which could include vitamin supplementation (vitamin E, and thiamine specially), hand feeding, braces...
Bathing in water is a ducks main defense towards mites and lice, so if he's not getting in regularly you're probably going to have to set him in the pool a couple times each week so he can clean himself off.
Dawn dish soap will clean the feathers, but it is going to strip the natural water...
Very likely you would be seeing some form of eye irritation by now if there was damage done to the eye after being sprayed. Since you are not noticing any, I think it would be safe to say he is alright.
In my experience, if they are acting normally, the coughing may simply be due to inhaling irritants into their airways. Things that often cause this would be dusty feed, bedding, and mold in their living quarters. This will usually go away on its own considering the cause is addressed. Some of...
Not all egg/laying issues are a direct result of imbalanced calcium levels. New layers often experience difficulty passing their first few eggs. Feeding a feed designed for ducks along with oyster shells, and allowing birds access outside to absorb sunlight will help ensure adequate Calcium and...
The bacteria is encapsulated underneath the tissue. Applying any topical ointment or spray will prove ineffective as none have the penetration needed to totally kill all the bacteria. Additionally, there is necrotic tissue present which will need to be removed to allow the skin cells to migrate...
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Occasionally a duck may lay a soft-shelled egg due to other reasons not associated with calcium intake. More likely there was a small glitch in her reproductive system that disrupted the egg formation process.
Unless this continues to occur regularly I would leave her be. If it...
I would try to get in contact with a local veterinarian familiar with poultry and hear out what their suggestions might be. Physical manipulation/fixator or surgical correction may be needed going off on how progressed the joint is at this point.
If none of those options are deemed feasible the...