Regardless of what is going on with her feathers, her diet is not good at all and needs to be changed immediately, because she's going to end-up with Fatty Liver Disease due to the fat content, as well as nutritional deficiencies due to not getting the proper foods she should be getting every single day...
***Any types of Dried Corn are horrible for captive/pet birds!!! Why did you think to add "dried, cracked corn" to her diet? Dried Corn, whether cracked or whole kernels, doesn't matter, contains absolutely no nutritional value at all, and is loaded with fat!!! Corn in any form is not even really a vegetable, it's actually a "Starch"....But any type of dried corn is worthless nutritionally, it provides them no protein, no vitamins/minerals/amino acids, etc., it only provides them fat and carbs that turn-into fat and that is stored in their liver...So please, stop ALL of the dried corn immediately, as this can definitely cause Feather-Destructive Behaviors down the road,
but more important is the Fatty Liver Disease, Diabetes, and Obesity it will cause!
***A great rule-of-thumb for any and all captive/pet parrots is that their regular, daily diet should contain NO Sunflower Seeds of any kind, NO Dried Corn of any kind, and NO Nuts of any kind, SPECIFICALLY NO PEANUTS! If you simply follow this rule and eliminate these items completely from your bird's daily diet, you're already ahead of the game...And depending on what seed-mix you're feeding her, it may also contain Sunflower Seeds, Dried Corn Kernels or Cracked Corn, and Peanuts....So you need to make sure that you're feeding your bird a healthy, low-fat seed-mix that is varied...No seed-mixes from Walmart or from a grocery store, they are all junk and they are the reason that most captive/pet birds die long before they should...
Sunflower Seeds and Nuts should only be given occasionally as "treats", and not every day; it's much better if you give your bird "treats" or snacks that they enjoy but that are also healthy, low fat, and provide her some nutritional value as well. Also, Peanuts are horrible for you bird, even as a treat, and should be avoided completely because they also often carry a form of Mold on them (grows inside their shells) that is very toxic to birds...Instead of Peanuts as a treat, give your bird a healthy nut that isn't a threat to her health and that provides her some nutrition, the best options being Almonds, Pine Nuts, Brazil Nuts, Filberts, Walnuts, and Hazelnuts....But NO Peanuts!!!
What exactly are you feeding your bird as her regular, daily diet? You said a "50/50 mix of Zupreem and Parrot Food"...What do you mean by "Parrot Food"? I'm assuming you're mixing a seed-mix with Zupreem pellets, but exactly what brand/type of seed-mix is it that you use? And what type of Zupreem pellets do you feed her? As far as Zupreem pellets go, the Natural-flavored and the Veggie-flavored are fine, but both the Fruit-flavored and the Nut-flavored are full of sugar, oil, and fat...and the sugar turns into fat and is stored in their liver...If you're giving her Fruit-flavored or Nut-flavored Zupreem pellets it's fine, at least she's eating some pellets, but if you're feeding her a junky seed-mix that contains Sunflower Seeds, Peanuts/other Nuts, and Dried Corn,
then you need to change that immediately, as it could very likely being causing her feather issues, and is most-definitely causing her Liver Issues.
****There are plenty of healthy, low-fat, varied seed-mixes available that are awesome to feed your bird, that they usually love, that will provide them with great nutrition and will keep their feathers, beak, nails, skin, etc. healthy and strong, and if you switch-over to one ASAP and stop the Dried/Cracked Corn ASAP, her Liver health will start improving immediately and her blood-sugar will normalize, her cholesterol will normalize, and her heart health will also improve. I highly recommend either Tropimix seed-mix, OR Higgins Vita-Seed California-Blend seed-mix...They are both available at any Petco and online at places like Chewy; neither of them contain any Nuts, any Sunflower Seeds, or any Dried/Cracked Corn; and they are both a mix of healthy, low-fat seeds, fresh grains and legumes, and dried Herbs, Veggies, and Fruit. I've never met a bird who didn't love them both (they are very similar), even the "seed-addicts", and you'll be improving her overall-health 100%...And neither is anymore expensive than anything else...and the Tropimix seed-mix also contains Tropican pellets in it as well, so if you buy a bag of Tropimix seed-mix and your bird likes the Tropican pellets that are in it, then you can actually stop feeding the Zupreem pellets all-together (I would ONLY suggest doing this if you are feeding your bird the Fruit or Nut flavored Zupreem pellets due to their sugar and fat content; if you're feeding your bird the Natural or Veggie flavored Zupreem pellets then you want to keep doing so)...
***Also, and this is huge by the way...Why have you stopped feeding your bird any fresh veggies? Your bird should get a serving of fresh-Veggies and fresh-Dark, Leafy Greens every single day in addition to her daily staple-diet of pellets and a small-amount of a healthy, low-fat seed mix![/B And while fresh-Fruit should NOT be given to your bird every day, but rather only 2-3 days a week and in small portions, due to the high amount of sugar that all Fruit contains, it's imperative to your bird's health that she get a good-size portion of fresh Veggies and Dark, Leafy Greens every single day!!!
Whether your Cockatoo has started over-preening/barbering/plucking her feathers due to her high-in-fat and low-in-nutrition daily diet, or it's due to a different issue such as boredom, which is quite common in Cockatoos, or it's a combination of both, you absolutely HAVE TO change-up her daily diet, because both her physical and her psychological health will deteriorate rapidly if you keep feeding her what you are...It's good that she's getting some pellets, even if they are the Fruit-flavored Zupreem that are high in sugar/fat, they are still also high in protein and contain a good amount of vitamins and minerals that she needs...But the Dried Cracked Corn that you've added to her daily diet is awful for her, and depending on exactly what type of seed-mix you're feeding her daily and whether it contains Sunflower Seeds, more Dried Corn, and Peanuts or other Nuts, this could very likely be a big part of her problems...And I don't know why you have "stopped giving her any fresh Veggies recently", but you really do need to make sure that she gets a good-sized portion of Fresh Veggies and Dark, Leafy Greens every single day...And the fresh Veggies and Greens are the least-expensive part of her diet!!! It's easiest if you make large batches of "Chop" out of an array of fresh Veggies and Greens, then put a daily portion into small, plastic freezer-bags, put the in your freezer, and then you can just pull one out every night and put it in the fridge to thaw for the next day...I give my guys their pellets and the small-portion of healthy, low-fat seed-mix that they get every day first-thing in the morning, so that they have that to eat throughout the day. And then in the evening when I eat my own dinner, that's when I feed them their fresh Veggies and Greens, usually in a form of "Chop", and we eat our dinners together...And then they also get healthy snacks/treats at night before bed, whenever we're doing any training, and occasionally throughout the day in small portions...For their healthy treats/snacks they get unsalted Almonds and Pine Nuts (my Senegal gets Nuts in-the-shell, as would your Cockatoo), they also get small pieces of fresh Fruit, such as Strawberries, Raspberries, BlackBerries, BlueBerries, Banana, different types of Apples, etc., basically any type of fresh Fruit EXCEPT for Avocado or any Citrus Fruits like Oranges, as the high amounts of Vitamin C causes enhanced-absorption of Iron into their bodies, and birds cannot handle much Iron at all, they develop "Iron Storage Disease", which is fatal...So any Fruit as long as it's fresh and no Avacado or Citrus Fruit...
They also get healthy snacks such as Dried Fruit like Banana Chips, Dried Pineapple, Dried Mango, and occasionally some Dried Coconut. The also love the fruit-flavored "Puffs" that are actually snacks for human Babies...Most human-baby foods/snacks cannot be given to birds because they usually contain added-Iron, but the fruit-flavored "Puffs" do not contain any added Iron, and they are all-natural, organic, and made from whole-wheat and real fruit...They come in tubes and are located in the babyfood sections, and come in Blueberry, Apple, Banana, Sweet Potato, etc. They get a few of these now and again, they are great "training treats"...