I noticed in his picture that his beak is kind of long. Assuming it isn't just the angle of the picture, you might consider a blood chemistry to make sure he isn't working on a liver issue.
Chances are pretty good he will allow you to pick him up some day. Just go slow and ask him first. He will step up when he's ready. Do keep him away from your child until you get to know his moods a lot better. Some amazons do really well with children. But yellow napes, particularly male yellow napes can be very aggressive and predictably unpredictable. They are capable of seriously nasty bites, so I would make sure your child knows not to stick his hands in the cage and be very careful about allowing your child to handle him. Frankly if I had a kid, out of my 5 amazons, I have only one that I would allow a child to handle and only in certain short and controlled situations.
For diet, Zupreem Natural is the brand I usually use. I do not get the kind with the pretty colors and honestly I think its just the people that like the pretty colors. The bird could care less and based on my own little bit of experience, I think some birds can have a nasty reaction to the artificial colors. Pellets are a good base diet but you should really be working on getting him to eat his veggies. I would guess that about 25-50% of his diet should be veggies and sprouted or cooked beans and grains. Since he's a rehome, remember unless he takes to those pellets right away you might need to gradually introduce them by slowly reducing the amount of seed until he is eating his pellets. Just dumping a bunch of pellets into his bowl might be dangerous if he's always eaten a seed only diet and doesn't know they are food. Mine also get a very large helping of veggies 6-7 days a week too.
