Combat seems mostly the same, with the notable change that enemy placement is more strategic. One new enemy type has a MASSIVE shield so you have to get behind it to kill it. Archers keep their distance better this time around. There's an enemy that buffs the hell out of the weaker ones around it. Stuff like that.
I can't speak to if there are other new areas besides it, but one of the central locations of the new DLC is a Grey Warden prison. It's a completely new area, not remotely recycled.
Influence on the story, I really can't say. The idea is that this DLC is a story Varric didn't want to tell because the lady making him tell stories wouldn't believe it, so it can take place at any point in the plot, other than the very, very, very beginning of course. Maybe it hints at DA3 stuff? Demo didn't show enough to really cover that.
Also, you get a new weapon that you customize as you play the DLC and you can use that in the main story.
EDIT:
My preview article