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. .
VA_M.O.N.E.Y.: I guess you have never been part of a turn based game site. That IS how things work. You have a time limit per move.
You will find it is RARE to NOT have people take a few hours before they move.. In fact it not rare that it be days between moves. That is the nature of the turn based game site. It is for people who WANT that type of flexibility. You need to choose your time limits wisely, ALWAYS expecting that many of your opponents could take the entire time allotted to them.