Challenges are actually planned for the next version. They'll be the first implementation of the tournament system (imagine them as a tiny tournament with just 2 players that launches as soon as everyone's registered)
They will be ladder1v1 games like any others (trueskill prevents "abuse" and actually encourages repeatedly playing anyone you wish).
Tournament / Game / Challenge Invites will be for online players only at the time being. We'll see about persistent / multi-day challenges later, but it's a good idea and thanks for bringing that up.
I don't think we need complex rules, though. I want challenges to be very easy to arrange, just rightclick a name, and they get an invite to an ad-hoc mini tournament that was created in your name.
That way, we can get a lot of the initial tournament code tested as well.