Answer:
I always run but never walk, I sometimes sing but cannot talk, No head on which a hat to place, You always look me in the face.
What turns from red to black as soon as it touches water?
What begins and has no end? What is the ending of all that begins?
As a whole, I am both safe and secure. Behead me, I become a place of meeting. Behead me again, I am the partner of ready. Restore me, I become the domain of beasts.
When set loose I fly away. Never so cursed as when I go astray.
Why was the cook arrested?