LONG POST INCOMING
My understanding of the trailer right now: "...forever without light." This suggests that at least a part of the game is set after the events of the first game, focusing on the Dark Lord ending. What about linking the fire? Well, remember that linking the fire would only delay the end of the Age of fire and perhaps there was no other undead powerful enough to get there after you. Looking back at the first game, most "powerful" undead have either gone hollow or didn't show any interest in prolonging the Age of fire.
The setting is obviously Lordran, although the Painted world of Ariamis appears to play a major role in the story. My theory would be that you start in the present, in the Age of Man - without light (fire). Most images where you carry a torch appear to be from present. The dragon skeleton found "somewhere", the area, which looks like Depths or Blighttown, what looks like Catacombs and so on. It seems that you come to Lordran from "somewhere", you don't just start there. The girl in the trailer may be your companion, who leads you there and tells you what to do or you just meet her there. About that later. So yeah, you're in the present, and in order to do whatever you need to do you must travel to the Painted world of Ariamis. Whether you use it as a time machine to get to the past is unclear. You certainly encounter the dragon, skeleton of which you've seen earlier on and it appears, that you encounter it in the Painted world.
A thing that is slightly confusing to me is - are all the snowy parts from the Painted world, or is the snow naturally occurring in Lordran, for the lack of fire?
Okay, now for the specific NPCs. The girl appearing in the trailer. My immediate thought when I first saw the trailer was "Daughter of Chaos!". Of all the female NPCs in the first game, her face reminds me of Quelaag the most. Might just be the art style though. The only thing (from my perspective) that goes against this theory is her clothes. If you pause the trailer right as the dragon flies by the main character and her, you can see that she's wearing a traveling mantle kind of thing and her actual clothes look kind of aristocratic. Dark base color with white sleeves and what appears to be a white collar. A popular theory is that she's Velka. The feather she gives you, however, looks more like an eagle feather, rather than something from a crow or a raven. It might be related to the bird you see at the very beginning of the trailer. Whether the feather is a lucky amulet she gives you or it fulfills some traveling role (i.e. summon the bird to fly to the "lobby" location) is unclear.
The dragon. The dragon is highly reminiscent of Kalameet. No glowing eye though and not as dark = not Kalameet, so I assume it's a dragon of the same kind, possibly related to Kalameet. My theory as to how you find him and how he dies: You go to the painted world, you encounter him, you go to the past, he goes with you, you kill him in the past, you find his bones in the future. Another option is that there's past and present Painted world but the basic idea remains.
The masked warriors. Their mask remind me of the crystalline masks. They might either be the generic enemy you fight throughout the whole game, like the hollows and undead soldiers/warriors in DS, or they might be some guardians of something. The one walking slowly in the rain appears to have some symbol on his pauldron, which suggests that he's like a warrior/assassin of "someone" or "something". For a while I even thought of the followers of the occult but there's not enough information about it in the first place.