Welcome to the community!
I have a long history of owning/breeding/hand-raising Budgies, and they really are no different than any other species of parrot, so try not to think of them/him as such. They are extremely intelligent, and also extremely social.
As far as diet goes, Budgies are a bit more difficult to get onto a pellet-staple, but what usually helps is to buy a seed-mix that has appropriately sized pellets in it. Usually these are going to be fruit-pellets, so higher in sugar, but the up-side is that the seeds in these mixes are on the lower-fat, healthier side. So look for the higher-quality Budgie-sized seed-mixes that also contain pellets, such as the Kaytee Forti-Diet (not their "Fiesta" mixes), the Zupreem Budgie mixes, etc.
***Try to stay away from giving him fruit every day, as it's loaded with sugar, and should be thought of as a treat, just like a millet-spray or a honey-seed-stick. What he should have every single day is fresh veggies and dark, leafy greens along with his staple of a seed-mix with pellets in it. Fruit should only be 2 times a week or so, and in small quantities. Budgies usually LOVE all of the dark, leafy greens, such as Kale, Bok Choy, Collards, Mustard, Turnip, Dandelion, Arugula/Rocket, Swiss Chard, etc. I just clip a large piece of dark, leafy greens to the cage bars at the end of a perch with a clothes-pin or clip, and they usually go nuts over it...Also love Broccoli if you just break-off the flowers into small pieces...With Budgies and food it's all about making it a small enough size for them to even attempt eating it.
Also make sure he has both a Cuttlebone and a Mineral Block.
***I always let all of my Budgies have one toy with a mirror in it or just one round mirror, especially in your situation where he's by himself and isn't yet bonded to you. They love a mirror, and it has never caused any of my Budgies to become hormonal or stop wanting to be with me. That's not how Budgies work. They love the cheap, plastic bird-toys, all of them, so as many as you can comfortably fit into his cage the better, along with one of those plastic bathtubs with the mirror in the bottom, I fill it with luke-warm water once a day for them, they love it.
Now as far as your bird in particular, Was he closely-bonded to your grandmother?
Did he regularly step-up for her and allow her to touch/pet him? Or has he never been a hands-on kind of Budgie with anyone? As already mentioned, most Budgies, especially if they come from a pet shop and not a private-breeder, are parent-raised and that is why they are not at all hand-tame. I have hand-tamed probably 50 or more parent-raised Budgies from the age of 16, and though a lot of people disagree with how I do it, it works quickly, does not hurt them in any way, and is temporary (about 2 months)...and that is by clipping their wings. When you clip their wings it does 2 different things, #1 it makes them much more willing to accept you helping them, for example they hate being on the floor, so a bird who would never before step-up for you will usually step right up the first time they are on the floor and you offer your finger to them. This builds trust quickly and lets the bird know that you are trustworthy and not scary or out to hurt them...and #2 it eliminates them constantly flying away from you while you're doing hand-taming sessions, and allows them to focus on working with you...Plus it eliminates you chasing them all around the room/house, which eliminates and ruins trust quicker than anything else...
If you do decide to clip his wings/have them clipped by a professional (it is totally a personal choice to be made by only the bird's owner), you want them to only clip the outermost 5-6 Primary Flight-Feathers on BOTH wings...This will allow him to be able to glide to the floor with total control, and it will ensure that his flight-feathers will grow back-in fully in about 2 months, which means you must take full-advantage of that 2-months that you have with him by doing hand-taming/step-up training/recall-training every single day, so by the time his wings grow back-in you will have earned his trust and he will be recall-trained, so that he'll fly to you when you call him and you will never have to chase him. Also, always do your daily training sessions in a room away from his cage, as that is his "territory" and his "safe space", and if he can see it he's only going to concentrate on getting back to it the whole time...You have to get him out of his comfort zone...