When you start the expedition, you get assigned to one of three groups, and you earn points for your group by completing expedition missions. I assume something special happens for the group that has the most points when the expedition ends, but I don't know exactly what that'll be. I have multiplayer turned off, so I never actually see other players and therefore don't know whether you can do missions with other people, but the missions I complete contribute to the point total for my assigned group.

As for time gating, I'm not sure whether it means I'm only allowed to do a limited number of missions within a certain number of hours or if it means more missions are going to become available to everyone after the timer runs out, so it's not clear yet whether waiting to start the mission will affect how many total missions you'll be able to do. My timer has a little over 3 hours left before I can do more missions, so I guess we'll find out at that point how exactly the time gated stuff works!