To find out what stairs you can currently challenge someone in, first go to the Main Stairs Page, then click on "Show your stairs only" link. The ones in BOLD are ones you can make a challenge in. .
In each stairs, it shows all active games - but would be interesting to see completed games also - see who was playing who & who won and such. Maybe not the complete history of games, but maybe the last month - or last 50 games completed in the stairs or something. (or all the games if possible)