Welcome to the forum!
I have a couple of older “rescue” amazons myself! I’m sorry if someone else already mentioned it, but if you plan on taking them with you when you move, an examination with a certified avian veterinarian would be a great way to rule out any potential health issues that might cause the stress of moving to be more dangerous than normal!
It’s ALSO very helpful in determining your parrot’s sex (this mostly matters in case of potential issues arising during hormone season from egg laying or aggressive behavior - when it comes to hormonal season, nobody does it like Amazons!), as parrots are not a sexually dimorphic species in behavior or physical traits (with some exceptions).
And finally - any time you change a parrot’s diet, please be careful! Abrupt diet changes are not safe, and can cause health issues and even death (not trying to scare you, it happened to me personally). It’s always important to slowly introduce new foods, and to weigh your feathered friend during the process so you can ensure that they aren’t abruptly losing weight. A kitchen gram scale and a simple wooden T-Perch is perfect for this! You may need to acclimate them first- our Yellow-Nape Amazon hated the scale and perch, and had to be bribed with treats.
Having a vet on hand for advice, tips, and to establish what your parrot’s body condition is like is so, so amazing!
Here is a compiled list of avian vet resources by country:
After a suggestion by a member, @Abu Colo, the Mod Team decided to create a list of veterinarians around the world who see birds. This was something we had discussed a few years ago, but the task seemed so large that we didn't get very far. However, the need is there and we decided that the time...
www.parrotforums.com
Don’t let that deter you from bringing them when you move, though. The Amazon in my profile pic has a boatload of health issues, and he handled coming home with me just fine. I really appreciate what you’re doing for Babe!
As for the feathers - I am not an owner of a plucker myself, and it is fortunately very uncommon for Amazons. Have you seen him/her actively pulling out/barbering her feathers, or just preening? I am of course limited by what we can see in the photos, but I’ve seen patchier looking Amazons in similar circumstances where diet and bathing are concerned. Our YNA especially looked rather sad before she had her first bath with us! If it is plucking, seeing a vet would be instrumental in establishing what underlying issues, if any, could be causing plucking (ex; sometimes there’s bacteria on the skin at work, and sometimes it is psychological).
As for the clipped wings - it took our Orange Wing about 3 years to fully grow his flight feathers after a particularly barbaric clip! We think it was due in part to the fact that he was, like your bird, a seed junkie, and seriously lacking in the kind of nutritional fortitude needed to inspire feather growth. This past year he EXPLODED with feathers everywhere, in the most massive molt I’ve ever witnessed, and now has a full set of functional flight and tail feathers. It was wild for a couple months though!