It is kind of hard to say what your bird is trying to tell you through its body language without being able to see it because it entails such things as the general posture as well as feather positioning and any movements that the bird makes at the time. Here is a link that can help you to begin to understand your birds body language, it shows budgies but the body language of your GCC will be similar to what is shown
http://littlefeatheredbuddies.com/info/ ... guage.html A scared bird will either try to get away or it may freeze, a nervous bird may pace or climb the cage but it will generally move away from you in the process The feathers may be held tightly against its body or it may briefly stand them up to appear larger than it is. A bird that is relaxed will not move away and may be slightly puffed giving the feathers a soft look and it will many times stand on one foot.
The baby begging behavior is just that begging and it could be for attention or it could be for food. Even though this bird is nearly an adult it may want some soft food just the same as a baby bird for reassurance. You could try giving it a little warm, not hot oatmeal, or whole wheat bread soaked in warm apple juice or even warm vegetable baby food when it does this begging behavior. Eating is a bonding behavior as well as a social one so it is always good to share food with your bird.
I have no idea as to the layout of your home or the room that your bird is in, but I would place my birds cage near a window with one side against a wall with the highest perch in the cage close to eye level. then I would place a chair and some sort of small table next to the cage. The reasons for this positioning is that the bird need the light from the window and will be able to see out of it without being directly in the sunlight, with one side against the wall it helps the bird to feel more secure as it can see anything approaching from three sides without worrying about something coming up behind it. The table and chair is largely for you and it give you a place to sit and read and talk to your bird as well as a place to put the treats that you have brought to share with the bird while you are doing this. It also gives you a place to fiddle with any toys that you want your bird to learn about such as shredding toys, puzzle toys, foraging toys and so on. It gives you a place to bring some fruit and vegetables to nibble on and as your bird gets curious enough to share with the bird and it gives a place near the bird where you can sit and look like you are not paying any attention to the bird where it can satisfy its curiosity about you by sneaking up to you and as it gets braver to start climbing around on you. All of these thing are to help your friend to forget about being afraid of you and learn to trust you in a manner that does not feel threatening to the bird. Later on it will give you a place to make toys for your bird or to introduce new toys to it as well as a place to begin training your bird.
Eating fruits and vegetables in front of your bird is the quickest way that I know of to introduce new foods o your birds and get them to start eating them. I don't like the current diet and from what you are saying it would appear that you don't either and based on where you want to go with their diet we are basically in agreement as to what they need to be eating. it might take a little bit of practice to adjust the amounts, but you could make a cooked blend of four or five whole grains and cooked vegetables with some cooked white beans and lentil so that it works out to about 40% cooked whole grains, 40 % cooked mixed vegetables and 20 % cooked white beans and lentils in small enough amounts to last for three or four days in a refrigerator and maybe and equal amount in the freezer of the refrigerator. I am encouraging this as free feeding seed mixes or pellets are not good for the bird, but they also interfere with finding and using any treats to help you gain your birds trust or for training it. This is due to the fact that for your bird a high value treat is one with protein and both seed mixes and pellets are high in protein. In this respect what you are currently feeding and the manner in which you are feeding it is working against you.