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. .
THE HIT MAN: It's all dependant on the timing. Each of you has a separate clock with your individual times. If your opponent moves 5 minutes after you do then he'll lose 5 minutes from his clock. If you take an hour to get back then you lose an hour. Hey presto he's got a 55 minute advantage.
If he makes a move just before you go offline for the night then that's a several hours advantage.
It's a good strategy to give priority to your Fischer's games and play as often as possible, even popping in for a minute at several points during the day just to check those matches. If you can arrange to get up several times during the night as well.... LOL.
You've got 500+ matches going at the moment. You might want to add your voice to the feature request that Fischer's matches be sortable to the top of the games list.