Players will be able to actively shape the economy of the world they play in buy trading the stocks of fictional companies within the game. That hasn't been decided yet. The main focus here will be chemicals. You can collect rent from your dwellers, a portion of which you must then relinquish to the government. You can have them mind your shop, carry things for you, accompany you on quests, etc.
Societies are groups of players working toward a common goal.
Societies can be a group of friends or business men with mutual interest. It is entirely up to you. The choice of how a society will be ruled will be up to the creators. The founders of the society will be able to choose how they rule the society out of a selection. Yes there will be a feature in-game that will allow society members to speak directly to each other at all times.