Budgies feathers and behaviour

by Gemma
(Uk)

Hi, We have just one budgie.
My budgie has recently seen himself in our large wall mirror (we forgot to cover it) he has seen himself a few times and has become interested in himself, when we try to take him away he tries to bite but eventually he moves, after this when in his cage he is fine (no calling out for "the other bird" the one in the mirror)
I don't know if it's related to the above but a few days after these incidents, his feathers have started to come out, possibly being pulled out. He doesn't want to come out his cage, (he does sometimes but not everyday even though we encourage him) usually he jumps at the chance to get out, he appears to be frightened of me and my husband.
I cannot see any bold areas on him, and he malted around 2 months ago.
He chats away when in his cage especially with background noise in the house, he plays with his toys (sometimes what seems to be violently, throwing his bells about)
He's munching on his cuttlebone more than usual too.
We are not sure of his age as we didn't buy him from a baby but the pet shop guessed less than a year old, (he didn't speak before we got him, he does now quite a lot)
His cere is bright blue so we know he's a boy

Do you know what is up with him, and how can we help him

Thank you very much for your time