Hello and welcome to the forum, glad that you found us so that we can try to help you develop a great and lasting relationship with your new friend. We will try and answer your questions and actually have a few of our own so that we can better help you and your bird.
First of all have you given him a name or did he already have a name when you got him and if you know it what is his age. Both of these are important bits of information if we are going to give the best possible answers. I understand that you said that he currently only eats corn, but this is totally an inadequate diet for him, so we need to know what foods you are offering him as well as when, please let us know. The more that you can tell us about both this birds past and his current lifestyle, schedules and so on the better answers we can give you.
Two weeks or even two months is like nothing to a parrot and except for stress this is especially true for the new parrot, who is normally very terrified for a period of time in its new home. Parrots do not handle change very well, they are pretty much a territorial species since they are prey animals. This is important to understand as they need to know what predators might be lurking in their environment, it is a matter of safety for them.
Depending on the parrots age, when you first get your bird and bring it home you are stepping into the role of either parent bird or possible flock mate or mate to your bird and after the bird knows that you mean it no harm, it will begin to trust you and come to depend on you for a portion of its sense of belonging, security and well being. The question that you have is how do you get to this point in the first place..
I apologise for this post as it could get to be rather long and I will try to keep it a bit shorter by providing a link or two to topics that might be useful to you and your bird where appropriate.
The first thing that you are going to need to do is get the bird accustomed to your presence and to the sound of your voice. To this end you will need to spend a considerable amount of time in the same area as your bird without trying to interact with it other than simply talking to him, using his name ( so that he learns it and knows you are talking to him), giving him a lot of " good bird" type of praise and dropping a treat ( such as a piece of almond) in his food dish now and then. While you are doing this do not look at him directly, instead look at him from the corner of your eyes, ( predators watch prey with a full frontal stare). These things will allow your new friend to watch you while you do things in the same room or area without putting any pressure on him and it will also allow him to get accustomed to the sound of your voice. Along with the occasional treat in his dish this will help him to relax and begin to look forward to your being in the same space as he is in and it will help him to see you as a giver of good things that he can eat. It will begin to help him to feel more safe and secure and start the process of earning his trust. You will know that this is helping as your bird will stop moving towards the back of the cage and will most likely start coming towards the front of the cage to see you when you enter his area.
After a week or so of doing this or when ever he stops moving away from you when you come into the room you can start the process of gaining his trust and hand taming him. Here is a link to help you with this process.
viewtopic.php?f=11&t=15840 Do not be concerned that the method outlined was written in response to another members question about a different species of parrot, this is the method that I have used with great success with all of my parrots and I have 5 different species of parrots.
I think that as far as giving him time out of the cage to fly and explore his area, I would start by only letting him out for a couple of hours just before his dinnertime, which should be about dusk. This is because that is when they normally eat in the wild, just before they fly to their roosting area to go to sleep for the night. This should make getting him back in his cage easier in the long run. If you are consistent with doing this he will learn to go back to his cage on his own about dinnertime. He will not do this right at first and you may have to catch him after it gets dark and putting him in his cage and allowing him to eat before turning the light back off so he can sleep, but he will learn this as part of his daily routine. Parrots love schedules and regular routines that they can count on as it helps to provide them with a sense of security and of knowing when certain thing will occur, a sense of some control over their own lives if you know what I mean.
Here is a link to toxic and non toxic items for parrots
viewtopic.php?f=8&t=12521 The actual list begins on the second page of this topic and it include woods, plants, foods as well as items that you may have in your home that you need to be aware of. The primary reasons for my including this list at this point is to help you to provide a safe environment for your bird as they are notorious chewers of things as well as to help you with your birds diet. Your parrot needs to learn to eat a large variety of fresh, raw organic fruits and vegetables as well as a limited amount of protein foods such as a few tree nuts and a good quality seed mix. Some people prefer to feed pellets over the seed mix, but I am not really a fan of pellets. The best way to teach your bird to eat this variety of fruits and vegetables is to eat them in front of him and then when he starts demanding some for himself, share some with him. The sharing of food is a socializing activity for parrots as they normally eat with their flock ( you) and is also a bonding activity. The best times to share this type of food with your bird is first thing in the mornings before you give it its regular breakfast, just before the bird takes its normal mid day nap and about an hour before the birds dinner time. This is usually an ongoing process since most breeders do not wean their birds to fresh raw produce, only to seeds or pellets. Parrots are taught by their parents what foods to eat, what these foods look like as well as how to find the foods. You will have to teach these things to your bird, even though the best time to do this has probably already come and gone. So do not get discouraged if the bird refuses to eat this food right away. I consider this process to be a long term thing just like cleaning its food and water dishes is or any of the other daily chores in caring for my birds.
I think that I have answered the majority of the questions that you have asked with what I do with my own birds and tried to share some of my reasons for the way that I care for my own birds. I hope that you and your bird find this information useful to you. Please feel free to ask any other questions that you may have.