But again, if you're going for the Marvel method..
Stop right there. Can't go any further because there simply isn't a Marvel method in place. DC is the alternative. If there was a Marvel method, then the people sitting at the end credits to Man of Steel would of got their fill of some kind of cameo, ala Marvel films. I think it's right for DC to go off and execute their OWN thing, which is what they seem to be doing with Superman/Batman.
1) How Superman's been doing since the last movie. Is he still saving people?
That's all inevitable and appropriate towards the continued story. It shouldn't be hard whatsoever for this film to address what's being asked above, especially in a 2 and a half hour movie, or whatever the running time may be.
Is he working at the Daily Planet?
The end of MOS clarifies this, as well as Amy Adams returning as Lois Lane, which should indicate some scenes with Clark/Lois inside the offices with its natural progressions and story building.
Any emotional scars from the insanity of the last movie
This could be dealt in how he handles the presence and threat of the Batman..
What about Metropolis, how's the rebuilding going?
The importance of Lex Luthor hinges on this question. Again, storytelling moving forward with Lex's involvement in how he views an alien walking amongst us in his city..
2) This new Batman. Who is he? How is he different from previous incarnations? Why should we care about him just as much as Superman.
Do we really need to know who he is? I mean, Bats is a dark character, one who lurks in the shadows and most of the time, can't be seen. His intentions or incarnations shouldn't be as clear as Superman's development....
3) Why Superman went to Gotham (or Batman to Metropolis) and why they're fighting.
All depending on the focus and nucleus of the plot and conflict surrounding the characters. If anything, I'd prefer the conflict to take place in Metropolis since this is set in Supes's world.
5) The overarching threat that forces them to work toward a common goal (presumably a new villian, who also has to be set up and characterized).
Did you see all those LexCorp placements in MOS? Yeah, those weren't by accident. Neither was the "Wayne Enterprise" logo....
6) Development for characters (like Lois Lane) that weren't fully developed in the first movie, plus any characters from Batman's world that might show up (Alfred and Gordon at the very least).
For Lois, see above. I'm sure she'll be an intricate part of the story since she DOES know that Superman is Clark Kent. This dynamic alone could be spectacular in itself. I'd prefer casts such as Commissioner Gordon or Alfred, if they go that route, shouldn't be a focal point, maybe quick cameo's or acknowledgement at best.
Remember, this is to introduce the new Batman, not necc his entire family or rogue's gallery. It's still Superman's world we're working off of and how the two could interact.
It will be very difficult, if not impossible
In Hollywood, nothing is impossible, dude. What you're going to have to do, is trust in this and have some faith. The payoff could be huge, and should be huge.