Thank you for bringing this little green man into your family and providing a good home for him!
In addition to information from Carolyn, you may find the PDR (Polly's Desk Reference) forum post about internet resources for locating avian veterinarians to be helpful, at least in locating backup vets or vets a nearby vet may wish to consult with.
As our other board particpants have advised, an overgrown beak could be a sign of liver problems, or may be due to your boy not having had appropriate surfaces to groom his beak upon - or a combination.
Since his diet has not been good, it is possible that it was mostly seeds. Seeds are a very poor diet for Eclectus (but OK in small amounts as treats) as they are very low in important amino acids and other nutrients while being high in fats and carbohydrates. Potential liver problems could stem from that diet, and could be significantly helped by a proper diet.
A seed diet is also very low in important antioxidants such as carotenoids and anthocyanins. These are found in foods that are red/orange/yellow and deep green/leafy in the case of carotenoids, and that are blue, purple, and dark red in the case of anthocyanins. A few examples of carotenoid rich foods are carrots, peppers dandelion greens, broccoli and yams, and foods rich in anthocyanins are cranberries, blueberries, blackberries (lots of different kinds of berries)- and dark red or purple peppers.
In a nutshell, an Eclectus diet should focus on fresh (or steamed/cooked) greens, vegetables, fruits and sprouts, with a small amount of a high quality seed and nut mix. The diet should be high in carotenoid rich foods, high in the natural fiber a fresh diet affords, and low in fat (NOT non-fat).
Please do not try to trim his beak on your own. Please have an avian veterinarian, or a vet with experience with parrots, trim his beak the first time. Then, be sure to offer him perches that are rough in texture - not splintery - just roughened so that they remind you of bark on a tree branch - so he can continue to keep his beak trimmed and shaped by natural rubbing and grooming behaviors.
When his beak is in proper shape, he will find it easier to eat and to preen, which should have a positive impact on his condition, his looks - and how he feels generally.
As far as keeping him in an aviary with other parrots, I believe it would be best for him to have his own aviary and cage, but he can be near or in sight of the other birds. He may very much enjoy seeing and watching them, but because of his size, he could easily injure them if he should become startled, frustrated, or get into a squabble over food or perching places.
Does he have a ring? When the vet examines him, please ask the vet to record his ring numbers (the vet will probably do this anyway) and see if there is a year on the ring. Often, rings contain the year a parrot was hatched, and the initials of the breeder or his/her aviary facility. The year on the ring will help you to have an idea of his age.
Please ask lots of questions...
Al and Mary
Cabby and Chardy (SIE)