Welcome aboard, Commander!
The galaxy is the same whether you're in Open, Private Group, or Solo modes. That includes the back story, the missions, the community goals, and so on.
The particularity of the Mobius group is that PvP is forbidden, except in conflict zones. See the
Policy page. That being said, you can still be attacked by NPC's (AKA AI's)!
And feel free to add your name to the
In game friend list thread.
Fly safe!