i know you can invade other players worlds if you wanna be an douche, but is possible to play and progress through the world with multiple players?

Yes, you can summon other players in to help you, primarily with the goal of killing the boss of an area.

If your in Human form you can find soul signs of other players. You can find soul signs anywhere really but in general you'll find soul signs either at camps or right before boss gates. Summoning other players is mostly about getting them to help with boss fights.

Absolutely. I plowed through all of the sewers with another player last night.

It's all random though, you are not able to to summon specific people.

There are co-op components, but it's not the same level you'd find in Halo, for instance.