Everyone, the OP lives in Tbilisi, Georgia (that would be in Asia, not the US), where the availability of pellets, CAVs (specialist bird vet) and proper toys is probably almost nil. If he's taking advice from a University animal department, then that's about as good as it gets.
It's OK for the bird to have seeds, but it would be far, far better if you gave him a diet based more on vegetables and edible flowers. In some places, you can buy special pellets that are designed to have everything in them that a bird needs. I am luckily able to get these pellets, but I know a lot of people in my country cannot. Believe it or not, plenty of birds can and do survive on an all-seed diet. Even though we know it's not the best thing, sometimes it's the only thing an owner can get!
Your bird is very, very young. In fact, he's probably too young to have been taken from his parents and may take some time before he learns to feed properly and to trust you. We can try to help you by answering your questions, but if he does get sick, what will you do?
I hope you will be able to find a much bigger cage for your bird. The one you have him in is likely to cause him to go a bit mad (just as you would if you were trapped in a tiny room). Alexes need a cage at least a metre high and wider than that if you can get one. My own cages are 2m x 2m x 1m, just as an example.
If a larger cage is not possible, then maybe you could allow the bird to be free in a smaller room in your house? It's easy to make an area just for him. You can make a perch from a piece of tree or hang ropes and poles for him to sit and climb on. If you keep your bird in that tiny cage forever, he will not do well. It might be OK for now while he's small, but an adult Alex would go quickly mad in such a tiny home.
I've just watched the first of the videos you posted (the other two have no picture). Your little bird looks quite fine and is very beautiful. I can't see anything odd in his breathing or the way he's perched, but he does look a bit stressed. Try keeping your voice low and soft, but speak to him all the time just as you're doing. He'll get to know you and hopefully begin to like you soon.
It's good that you're asking questions. We'll all help as much as we can. For now, I'd suggest you find out which vegetables your bird likes to eat (don't give him avocado - it's poisonous) and maybe offer him some tiny pieces of peanuts or cooked egg. My Alexes like the seed heads from the grass that grows in my garden.