Re: question about introducing a new bird...
Hi Kikii, welcome;
The "dandruff" you are seeing is probably keratin coming off of new feathers. Keratin is the sheath that forms around a feather shaft as it grows in; when the new feather comes in, the keratin flakes off. New feathers can make a bird very uncomfortable, though giving them water for bathing seems to help.
Traci is correct about the need to quarantine your new bird away from your current bird for no less than 45 days; some vets recommend longer. That's because it can take some illnesses that long to incubate, during which time they are undetectable but still transmissable to another bird.
After the quarantine is over, we recommend putting the birds' cages next to each other so that they become more used to seeing each other. After they seem comfortable with that, then you can start introducing one to the other's cage. It is a slower process but it has more positive results -- and less potential injury due to squabbling.
Oh, and to answer your first question: Yes, birds can become very jealous. :eek:
Best wishes,
Barb
Happiness is a firm banana