You should ALWAYS have a new bird taken to a certified avian vet directly after bringing him home, and this one is 20 years old and most likely hasn't had a wellness exam or blood work in a long time. The reason it's important to to take a bird that is new to you for a wellness exam that includes blood work, cultures, fecal smear, etc. is twofold; You'll discover any active infections or disease processes the bird may be fighting and get treatment for them, and very importantly you'll get baseline test results to compare future test results to if he ever becomes very sick or develops an issue like diabetes, etc. I don't know if you're aware of how birds hide all signs and symptoms of illness and pain until they can't hide it anymore, so by the time a bird shows any outward signs or symptoms of illness or injury the bird has been suffering for quite some time. It's instinctual, a survival technique in the wild that they all possess. So you can't ever take a "wait and see" approach with your bird, as the first time you notice something wrong is likely a month or more into the problem's progression.
He could be barbering his tail, he's in a new home, his prior owner of years and years is gone, so this can obviously cause stress and behavioral issues. That being said, PLEASE get him a MUCH LARGER cage!!!
If you can still get his original cage back please do that!!! Not only is that little, tiny cage you have him in inadequate and cruel, but if he could remain in the same cage (his safe place) he has been in for years and years his stress will be much lower. Imagine what he's going through! His owner for most of his life is gone, he has been moved out of the only home he knows, he's around all new people he doesn't know or trust, and then his safe place, his actual home within his home was taken away from him...Then he was put into a cage that is hardly large enough for an American budgie! Getting his original cage back with all of his original toys, perches, food dishes, anything that has been his from his former life will lessen his stress.
Even if you've already gotten rid of his original cage, toys, etc. you need to get him out of that tiny little cage immediately and get him into a very large cage the size of the one he was in! There's a reason he was in a cage that size! And he must have lots of toys and foraging activities to keep him occupied; parrots are very intelligent and they get very bored very quickly if they do not have toys and games to occupy them, as well as hours of out of cage time every single day! Especially now I'd make sure he gets a ton of time out of that cage, it's not even a quarter of the size of the cage he should be in!
I would make getting him an appropriately sized cage, like the size he was in his entire life (preferably that exact cage) priority number one, like today! Please don't just talk to your grandmother about it, it needs to happen now! She'll have to make room for that size of cage, that's a must. So before you do anything else get him that size cage and many, many toys, games, etc. to keep him busy and to lessen his stress. Being in that tiny box is not only physically hurting his tail and feathers because he can't even turn around, open one of his wings the whole way, sit up correctly, etc. but the size itself is also stressing him, no toys is stressing him, he's bored, cramped, scared, etc. You couldn't even fit a single toy in that cage with him, if you have then the space he has is even worse...
Second priority is finding him a Certified Avian Vet immediately and getting him in for a complete wellness exam, blood work, etc. Usually I suggest seeing the vet as priority number one but not in this case, he just cannot be kept in that cage any longer! I'm not trying to be harsh or mean, or seem hypocritical, you're obviously new to keeping a parrot, let alone a parrot with the size and intelligence that a Ringneck or an Alexandrine has.
"Dance like nobody's watching..."
