Answer:
What sphinxes employ and players enjoy.
They come out at night without being called, and are lost in the day without being stolen. What are they?
Every country has one, though we are not the same. Waving to our citizens, throughout the wind and rain. What is it?
Temporary evidence of where you've been strolling
What goes up but never comes down?
I am a room that has a roof but no walls. What am I?