Without a form of identification with a year attached to that ID, no one can really begin to guess how old Melika is. An avian vet may be able to guesstimate, but they could be off by several years!
She's gorgeous!
As far as feathers go, try giving her a bath via a spray bottle, under the kitchen faucet, in the bathroom, or however she likes it best! With preening, she may sort out her feathers. For the most part though, they appear fine!
Diet? If available to you, an organic dye/sugar-free diet, along with healthy nuts, sprouted seeds, vegetables, some fruits, healthy grains, healthy legumes, occasional cooked eggs, etc would be a pretty good base diet!