Answer:
A type of hammer that brings a room to order.
What can go through glass without breaking it?
I am the heart that does not beat. If cut, I bleed without blood. I can fly, but have no wings. I can float, but have no fins. I can sing, but have no mouth.
My first half is normally made of stone, my second is crazy, and I taste sweet when complete.
Hands she has but does not hold. Teeth she has but does not bite. Feet she has but they are cold. Eyes she has but without sight.
What sphinxes employ and players enjoy.