I commented on your other thread. The drake issue makes more sense as to why she is having issues.
On your other post, I stated that I don't think its wet feather and I still don't. The condition of her feathers look good. Check her preening gland, you should see a dirty gland vs a nice clean one if having issues with it. A warm cloth can often dislodge any grime without the use of soap. Soap would be the last alternative. And even then, you only need to wash the preening gland.
Drakes should have at least 4 hens. The overmating could definitely be causing the discoloration on the bill as well since drakes tend to pull skin and feathers of the head.