So if I want to notify people about their matchup, showing the current one, can I just assume which matchup it is depending on the tuesday to monday time constraint?
Well, if you want to get the current matchup, you can just ask for "week=current" -- most of our date based services should respect that. I mean, you'll also get the current week if you just ask for the scoreboard without a week specified, but I guess the week=current makes it feel more official. We also have a start_week, current_week, and end_week in the league XML.
CODE
http://fantasysports.yahooapis.com/league/<league key>/scoreboard;week=current
And we'll tell you which numeric week that it is in the XML response, so there really shouldn't be any guessing involved. As for your question about when week 1 starts, no, there isn't any other value currently in the services that exposes that.