I don't understand how visiting them at camp is that different than visiting them at the castle, still. It's still totally outside of the actual quests. It's just the same thing with a different backdrop. 
It also allows for more variety in the interactions. If you can interact with them in the camp, they can discuss the questline for that region as it progresses and, depending on the story, possibly have a larger role by accompanying you at some point (not as a companion, more like a "they show up in the climatic scene/dialogue" kind of thing). Then, when you come back to the Keep, there could be an additional set of interactions.
That seems to imply at least a 2/2/2. It could be more than that, even. I doubt it, but it can.
Yes, this seems to imply 2/2/2. I agree that I really doubt that there would be more than 6, given earlier statements about having about the same resources for romances as in DA 2. I'm thinking 2 gay, 2 straight, and 2 bisexual. And the best part (for me at least), is that with Cullen being an NPC and almost certainly being either straight or bisexual, it's looking more and more likely that we'll finally get our first gay male companion! There's a silver lining in all this!