Much better explaination than mine
Teams are a "for fun" feature, something people requested long ago. People used to form teams for things like Folding@Home and Seti@home so they could compete as groups / communities. They offer no benefit, they're just something to view individual rankings for a team, or compete as a group against another team.
As for satoshis trickling in while your miners are offline, PPLNS is a time-delayed payment method. This means you start out with low rewards (since you only have shares in a few shifts), and eventually those rewards grow as you have shares in more shifts (up to 10). When you turn off, you still have shares in shifts and rewards continue to trickle in until all of those shares have expired.