Not for a game I have, but a game I'm currently developing after many years of attempts, but failures.
1) Very very important.
2) No. The game is built around building your empire. The social aspect is designed to be a major component of this.
3) Resource bonuses that can be given by friends (but cost the giver nothing), information exchange, count-strike buffs for attacking someone who attacked an ally, sense of protection when belonging to a group, group based techs, group based buildings, group based artifacts.
4) Maximum cap on group size for factions, trade partners, etc (which can be increased through tech).
5) No
6) Irrelevant.