The name of the "big bird" (Hippogriff) is Buckbeak. Hopefully this is helpful!
Avifors
John Williams did, and I might add, he was bloody brilliant!
Phoenix: A legendary bird that does not live on fruit or flowers, but on frankincense and odoriferous gums. When it has lived five hundred years, it builds itself a nest in the branches of an oak, on the top of a palm tree. In this it collects cinnamon and spikenard, and myrrh, and of these materials builds a pile on which it deposits itself, and dying, breathes out its last breath amidst odors. From the body of the parent bird, a young Phoenix issues forth, destined to live as long a life as its predecessor. When this has grown up and gained sufficient strength, it lifts its nest from the tree (its own cradle and its parent's sepulcher), and carries it to the city of Heliopolis in Egypt, and deposits it in the temple of the sun.The Phoenix is a mythological bird, said to burst into flames when it died. It would then rise from its' own ashes with new life.Professor Dumbledore (from Harry Potter) owns a pet phoenix named Fawkes. Harry's wand's core is made of Fawkes' tail feather. He also gave another tail feather to the wand which Lord Voldemort carries. Fawkes leaves when Dumbledore dies.
Little Bird
No, the phoenix is a mythical bird.
Big Bird
Bird's feet are not mentioned in Harry Potter and the Philosopher's Stone. There is no reason for them to be anything other than the feet of a bird.
A phoenix.
Harry Potter's owl was named Hedwig.
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Avifors
Fawkes burned up in Harry Potter 2 because he is a phoenix, and when they get old, they disintegrate and are reborn from the ashes. It's kind of creepy, actually.
A Series of Unfortunate Events, Harry Potter, May Bird,
A Phoenix named Fawkes.
Buckbeak is a creature that Hagrid has in a magical creatures lesson in the third harry potter movie. To most, it would seem it is a mixture of a bird, and a horse. the proper name of this creature is a hypogriff.
I think it's a phoenix :)
I think you are talking about the raven, which symbolizes death. It can be seen when buckbeak is killed.