New 5-6 month old alexandrine parrot

Hey guys, I have just received my 5-6 month old alexandrine parrot but I have noticed a few things that are worrying me. Firstly is it normal for a parrot to be shaking every time you look at it or come close to it (also the bird was delivered to me over the course of a full day) and also is it normal for young alexandrine parrots to have a grey patch on their wings? I would appreciate if someone could answer as quick as possible.

Welcome to Parrot Forums!
On the behavior side, yes it can be normal for a Parrot to shake and show signs of fear when Humans look or come close to it. Unlike cats and dogs who have been with Humans for 1000's of years to be part of Human gatherings, Parrots have not.
Consider a total restart where you slowly approach your Parrot and sit along side the cage and read softly out loud to your Parrot. Consider the Large Thread in the Amazon Forums found at the top of that forum highlighted in light blue Title: I Love Amazons - ... This massive Thread will provide you extensive knowledge in the care and loving of Parrots and your Parrot will become more comfortable with you being around.
It is also important that Humans understand that the Parrot has no reason to trust Humans. That trust bond takes time to develop. In addition, Humans have high expectations that the Parrot is a fluff ball just waiting to be handled and loved. You need to prove to your Parrot that you can be trusted.
I hope that this helps with the first part of your question.

Welcome to the community!

As Sailboat already mentioned, the bird is new to you and your home, so yes, it's going to take time to just settle-in to it's new home...But more of the reason for it's fear of you is probably that it either wasn't hand-raised/hand-fed by it's breeder, or at 5-6 months old it's possible that it was originally hand-raised/hand-fed as a little baby, then once it fully-weaned the breeder spent little to no time handling him or with him at all, and that time period between when the baby weaned and when you bought him served to cause a regression in his level of tameness (Alexandrines wean around 13 or so weeks old, so he's been weaned from quite a while now, and may not have been handled or interacted with for months).

So as Sailboat mentioned above, you're going to have to approach hand-taming your Alex from the view that he is a young, juvenile Alexandrine who has had little to no interaction/contact with people, and who is extremely scared of people, and who is going to need a good bit of time to give you his trust and feel comfortable with you being near him or handling him. You can help the process along by making sure that you locate his cage in the "main-room" of your house, which is the room of your house that you spend most of your time in whenever you're at home. That way even when he's inside of his cage and you're not directly-interacting with him, he's still going to always be near you/around you, he'll hear your voice all the time, see you all the time, etc. The last thing you want to do is put his cage in some spare bedroom or room of your home away from where you usually are. So whenever you're at home on the computer, watching TV, Reading, playing games, etc., he needs to be with you so that he'll start to feel comfortable with you always being near him. And then it's just a matter of going very slowly, at HIS PACE, not your pace as far as you touching him, him stepping-up for you, etc. You'll need to work with him each day, but you need to start out very, very slowly, and since he's really scared of people you need to start out by simply sitting next to his cage talking to him, reading to him, etc., and maybe trying to feed him treats through the cage bars...I'd keep your hands out of his cage except to feed him and give him water until he settles-in and gets used to him just being around you...It's going to take a good amount of time for him to become hand-tame, so keep in-mind that it sometimes takes months and months before a non-tame parrot will even step-up for you, that's normal, and trying to push them or force them to do it will only make him even more afraid of you...

As far as the feathers on his wings, could you post a photo of what you're talking about? And do you mean that a patch of his actual outer-feathers are gray, or is this a patch where he has no outer-feathers and his down-feathers are exposed? Because their down-feathers are gray, so if for some reason he has a patch where he's missing actual feathers then yes, the soft, fluffy down-feathers underneath the actual feathers are gray...