Welcome to the forum! It was real good of you to take Chewy from your friend but you really bit quite a large mouthful because cockatoos are the most difficult of the large parrots. Having said that, it's not impossible to keep them healthy and happy if you put the time and work into it. There are three essential points to follow with them:
1. A super strict solar schedule with full exposure to dawn and dusk [they are short day breeders and have two breeding seasons during which they naturally become a bit difficult but they are practically impossible to handle when they overly hormonal]
2. A fresh food diet [cockatoos consume A LOT of produce and need it every single day] and lots and lots and lots of chewing material.
3. An inordinate amount of time spent with them both out of cage and one-on-one and strict and completely unchanged routines.
Now, a word of caution, she has not bonded with you or your wife. She is in what we call 'the honeymoon period' where she is beginning to learn about her new humans, home, routines, etc - the bonding comes later and it takes months and months. Furthermore, parrots always behave their best during the honeymoon period so don't get discouraged if she starts getting even more aggressive with you in a couple of months or so - it's normal.
A solar schedule is something that people usually think they understand but, in reality, they don't so, if you have done research and know about avian photoperiodism, skip this part but, if you don't know about it or still have doubts, read on. Birds are photoperiodic - this is a long word that means that their bodies know what season it is [courting, nesting, breeding, molting, etc] from the length of the daylight hours. In order for their bodies to know how many hours of light are in the day, they need to be exposed for, at least, 1.5 hour of twilight both in the morning and in the evening [well, this time of the year, it's not the evening but the afternoon]. Birds need good light to see properly, to regulate their moods and their endocrine system. It's the way nature evolved them and not my personal opinion. Because they are the most vision-dependent of all the vertebrates and because they can see better, more accurately and more colors than mammals do, they need a good quality full spectrum light when indoors [the specs you will be looking for are a CRI as close to 100 as you can get it but not lower than 92 and a Ktemp not lower than 5000 but not higher than 6000]. Now, their endocrine system needs to be exposed to the different spectrum that happens during dawn and dusk because it is this special light that turns on or off their 'internal clock' [pineal gland] and the number of hours between these two events is what marks the different seasons for them. This time of the year, I uncover my birds cages at 6:15 am but do not turn on the artificial lights until 8 am - then turn off the artificial lights at 3:00 pm and feed them dinner right after that. I cover their cages at around 6 pm when they are all fast asleep in their roosting perches [I use quilts and bedspreads for the covers because they are large and thick enough to prevent all light from 'sneaking' into their cages but I also never turn on any artificial lights in the rooms where they are kept and have a black-out curtain covering the entrance to my kitchen because there are studies that tell us that the merest sliver of light affects them].
Cockatoos eat A LOT of plant material - so much so that they are the ONLY species of parrot that, in my personal experience, actually go for the greens before they go for the fruit or veggie. I feed mine a leafy green [or raw broccoli but, when it comes to leafy greens, they prefer the ones with crunchy stalks like bok choy, Swiss chard, nappa and the very heart of the romaine], a raw veggie and a raw fruit with gloop [this is a dish made out cooked whole grains mixed with chopped veggies - I've been doing research on parrots natural diets for over 20 years and have long ago reached the conclusion that pellets are not and never will be the best dietary option for them, I can elaborate on this if you are interested]. For dinner, mostly nuts and a few seeds [all my birds get a multivitamin/mineral supplement twice a week and extra dosages of calciboost for the laying hens].
There is nothing more important for undomesticated species kept in captivity than a steady, unchanging daily routine. Parrots don't live in hierarchical societies so, to them, obedience and subservience are concepts that cannot be understood as they all make their own decisions so, when we take away the power to decide what to do when, we cause them a lot of stress. Following the same biorhythms they would follow in the wild helps reduce stress - and the fact that they learn the routine and can then predict what will happen when, gives them a sense of control over their own lives -again, stress reduction. My birds get their cages uncovered and open when there is just a little bit of light on the horizon, about 1 hour after this, when there is already good light, they get their produce, half an hour after this, their gloop and they are then put into their cage to eat breakfast. About half an hour after this, their cages are opened again and they stay out and with me until about 1:30 pm this time of the year [it's later during the long days of the summer] and I already told you that I turn off the lights and give them dinner at around 3 pm.
The best time of the day to interact with them is after breakfast and before dinner but, when they are out, they are always interacting one way or the other [mostly me running around taking things from them or preventing them from chewing something they should not be chewing
].
I would NOT recommend you take your bird out without a harness. Parrots are not dogs, they are undomesticated animals that do not have it in them and cannot learn to be obedient up to the point that they would not take off to look for a mate when hormonal. Even professional trainers [the kind that give shows] lose birds they free-fly.
Cockatoos can be the sweetest things or they can be completely unpredictable and aggressive. It all depends on the care they receive. Give them what their bodies and minds need and they will repay you with love. Parrots are not naturally aggressive [they are not predators or live in a hierarchical society where they have to fight for their 'place'] and they only attack defending or protecting their nest, their mates and themselves. Unfortunately, they can also learn to bite in order to get their point across because people who don't understand them teach them. These humans don't mean to cause the bird harm and they don't do it on purpose but, like I told my kids and now tell my grandkids, "Sorry, I did not mean to" doesn't walk the dog - and the result is the same: pee on the floor and a dog that did not learn to go outside.
So I suggest you start with her 'the right way' as soon as possible because although the days are now getting shorter, this will change very soon [the winter solstice is on Dec/21]. Mind you, you will not notice a change right away because the more messed up an endocrine system is, the longer it takes to go back 'on track' but you need to start somewhere.
As to her plucking, keeping her to a solar schedule, giving her a fresh food diet [cockatoos fed most pellets tend to have subclinical chronic dehydration], and having a strict routine plus lots and lots of chewing material [I suggest thick cardboard boxes and pieces of untreated 2x4] will help a lot but it might not completely 'cure' her of the bad habit because it becomes second nature to them [kind of like people who chew their nails]. I took in a 25 year old male LS2 that had very few feathers on his body, showing large areas of naked skin [belly, chest, back and back of wings, etc] and no wings or tail feathers and he now has his body completely covered [although not all of it with contour feathers] and just his chest shows skin - he had also allowed all his primaries [the long feathers in the wings and tail] to grow after his last molt but he has now been barbering them
Not that I am discouraged in any way because, based on my personal experience with extreme pluckers, it takes them years to get a better plumage and some of them never quite stop although ALL of them improve with good care. So don't lose hope if she keeps on doing it - as long as you see the smallest improvement and this improvement remains, you are on the right track.