Lindsay, I'm sorry that your question wasn't answered in a timely manner. We don't have many avian vets on this site.
Nutritional imbalances are a common cause of illness in our pet birds. Seeds should compose less than 20% of Lucy's diet. A diet of mainly seed and nuts has excessive fat, carbohydrates, and phosphorus; marginal protein; adequate vitamin E, and are deficient in amino acids, calcium, available phosphorus, sodium, manganese, zinc, iron, vitamins A, D3 (necessary for efficient absorption of calcium), K, and B12, riboflavin, pantothenic acid, choline, and available niacin. Ideally, a balanced pelleted diet such as can be found here: www.harrisonsbirdfoods.com or here: www.lafeber.com/pet-birds should be fed as well as hard boiled egg yolk, pancakes and cornbread, the tops of fresh greens, dairy products such as yogurt and cheese, fresh fruits such as apples, pears, melon, kiwi, and berries, vegetables such as broccoli, carrots, beets, asparagus, cabbage, sweet potato, and squash, and even tiny pieces of meat.
I'm not sure what a "duff" implies. Please clarify. Mites are not a common cause of feather problems in budgies and if your others aren't affected, mites are even less likely. I suspect that when she's eats a better balanced diet, she'll be able to replace her feathers more efficiently. A crusty cere might indicate benign cere hypertrophy, cnemidocoptic mange, or hypovitaminosis A. A water soluble vitamin product such as Oasis brand should be considered at least until she's eating properly. Can you upload a photo(s) of her face to our conversation? You can use the paperclip icon in the toolbar above your message box (if you can see that icon) or you can use an external app such as dropbox.com/
I can be more accurate if I can see what you're seeing.