What can I do for my sick parakeet?

I have a 6 year old male parakeet named Misty. I believe his specific species is the recessive pied parakeet but I'm not entirely sure. About two weeks ago he got one of his tail feathers stuck on a toy in his cage and being stuck scared him so he pulled the feather out. The place where the feather had been didn't stop bleeding for a long time but after that he was fine. Then about a week after the tail feather incident he started losing all the downy feathers near his vent. Since then he has progressively become weaker, lost his sense of balance, stopped vocalizing and now he spends most of his time on the bottom of the cage in a hunched position. He still eats a little, and poops normally but I haven't seen him drink much lately. He also spends a lot of his time drifting off to sleep, but he never actually falls completely asleep he is otherwise he is alert. He used to be the dominant bird between him and his cage mate (same age, gender and species), but now his cage mate pushes Misty around. We're probably going to take him to an avian vet in a few days, but is it already too late for my little Misty? If not does anyone know the cost of a vet appointment for a parakeet, how much treatment may cost, or what methods vets use to put parakeets down?