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. .
crosseyed: It would be very difficult to time out if you played several times a day
But it does depend somewhat on when you play, if you make a move and go offline right away, and I move right after this.... but you also get 3 hours added to your time every move, so several moves a day should leave you with more time, notless.