You cannot advance the story in multiplayer. Host can choose any region and map he has access to except a few single-player specific stuff. Its mainly for gear, leveling, grinding quests, etc.

oh, so only for current mission rewards, not for doing new ones.
but if my friend is the host and he have more completed story, i can still join in and get levels/rewards or only the host is getting those? (like, i'm only a helper)

yes, everyone benefits. rewards are shared and same with exp and whatever. For non-bosses, you a player will have to land at least one blow on an enemy to be considered part of the exp rewards.

oh, so it's like 50/50 reward, not based on damage, good. we could even exchange items?

Well, materials and money can be exchanged. Weapons and armor will most likely will have to be in fields or fighting the NMs and HNMs