If you log on to the game at load all your scores are sent to friends to try and beat in their own single-player environment. Party Mode has offline pass-the-controller challenges, and there are online ones too.
As for online, you should be able to join your friends if they're on a server. Could have swore I've done that.
Redwings, I suggest you do the Time Road Rules. You really get to know the layout better, and some on/offline races have checkpoints, giving you structure in the open world environment. You may also be able to create your own online checkpoint races, but don't quote me on that.