Mythical bird of prey

Answer 1

The winged lion is a Venetian symbol of royalty. The closest match I can find is the griffin or griffon - a mythical creature that is part eagle, part lion. However, it would be a lion with wings *and* the head of an eagle. It's a manticore. They can have wings, bat wings or bird wings. They have scorpion or dragon tail. Often depicted with human face. In some cases they are called wyverns, but this is a mistake in nominclature as wyverns are members of the dragon family.
Probably the sphinx. It has the body of a lion, the face of a woman, wings, and a penchant for telling riddles.

Answer 2

• Thunder bird
• Roc (although this may be based on the elephant birds of Madagascar)
• Phoenix
• Terror Birds (although these were actual birds that became extinct)

Answer 3

Sphinx, said to have the body of a lion, the head of a woman, and sometimes wings.

or:

Gryphon, a beast with the head and wings of an eagle and the body of a lion.