No, it is not. Although it is very common in Washington state.
they are well, look like this:
A Cedar Waxwing.
In the United States, it is illegal to keep native bird species as pets.
cedar waxwing
Do a Google Image search for juvenile cedar waxwing. Also, it would help if you told us in what country, state, etc... you found the bird.
I believe that you are talking about the waxwing. There is the Bohemian Waxwing which is grayish brown and the larger waxwing. The Cedar Waxwing is smaller than a robin and more of a brown tint than the Bohemian Waxwing. They both have the black eye band, or mask, and they have a yellow band on the tip of the tail.
Any cat that can catch it. For instance, my Maine Coon killed a Cedar Waxwing. It is currently in my freezer.
If you live in Europe it could quite possibly be a redwing.
it can "go"
The bird you are describing sounds like a Cedar Waxwing. They have distinctive yellow-tipped tail feathers and a pointed crest on their heads. They are slightly larger than a sparrow and are known for their sleek appearance and high-pitched call.
If you are in the United States, it is illegal to be in posession of native bird species unless you are a licensed wildlife rehabilitator or zoological park. You shouldn't be trying to feed a wild baby bird yourself. Contact your state's department of natural resources.
cedar waxwings eat fruit like pears cherries etc.