Hello and a warm welcome! Thank you so much for adopting a quaker parrot in need of a better home. What is your new bestie's name?
A lot of what you will learn about parrots will apply to all or most species including quakers. But, quakers are a bit different from other parrot species in several ways and unique in one big way, in the wild, quakers build communal nests, they use sticks to build amazing structures, according to the size of the flock, there are almost always chicks in the nest. Quakers are hardy birds, in fact they are illegal to own in several states because they escape, form their own societies and in some people's opinions become a nuisance species. These birds are scary smart, I have three quaker parrots, I'll never admit to being partial but I adore my quakers. I'm amazed at how the characteristics of the wild flocks carry over to the quakers who share our homes. I've heard again and again, "quakers are cage territorial". I agree, they will aggressively guard their cages and greet intruders with those bloodthirsty little beaks. Once away from their cages, you will see an attitude change, from experience it's better to let your quaker approach you.
Time, patience, respect. Your bird's concept of time is vastly different from yours. Your bird is probably justifiably angry, give him time to adjust and new reasons to trust.
Handling, it is very important to some owners to handle their birds, generally speaking, quakers aren't cuddly birds, most are far from it. Many people have had success with target training and or clicker training, I'm not one of those people. The closest I have come to target training with a quaker has happened a few times with my girl. She loves my Umbrella cockatoo and if the chance presents itself she will perch on top of the U2's cage and glare at me knowing I can't reach her without a stool, Harry is a talented pilot and moves much faster than my U2, still I usually panic and grab a dowel perch and attempt to remove her from harm's way. Harry runs for the perch, runs down the perch and attempts to amputate my fingers. I can only imagine showing Harry a clicker, I'm pretty sure she'd make me eat it. I guess it comes down to what works for you and your unique quaker.
I don't mean to imply in any way that your quaker can't be trained just that it may take more time than expected. My quakers talk, two of them are potty trained, we play games together, they come when called and go inside their cages when asked to. All three have shoulder privileges to a point, I only have two shoulders so they take turns knocking each other off my shoulders, this often leads to lots of swearing (from the parrots not me) occasionally a skirmish ensues that ends in a time out for one or more quakers.
Diet is so important, start offering new foods now but be sure to offer the familiar food you know your quaker is eating. Some quakers will go to extremes while on a hunger strike. Offer a variety of vegetables, pellets, a little fruit, pasta, etc. Don't give up, most birds will eventually get the hang of a healthier diet and it's well worth the effort, your bird will benefit for years to come.
Best of luck, looking forward to hearing more about your adventure.