Are there quests?

Not in the traditional sense. Instead of looking for quest-givers to give you things to do, you can select an available mission, from the high command during a campaign, and join a PvP battlefield or a cooperative horde map in order to achieve it.

We’re currently working on short, horde-style firefights as our main PVE content for launch.

Of course, you can always look to the community channels and your faction leaders to get some direction. In addition, there are mid- and long-term opposed goals for factions that appear on a regular basis as part of the ongoing server-wide campaign system.