Just cut over from V to IV BtS. Lots of little differences. There's suppsoedly a tutorial in IV, but I guess with BtS thats not present anymore. Questions:
1) Is culture good for anything besides border expansion?
Yes. There is a cultural defense rating that aids in the cities defence. Also, the cumulative culture of your civ adds to your overall score.
2) How far from your city will citizens work? Is it two or three tiles?
It is a Big Fat Cross(or Plus) extending two tiles out in each of four directions. Note that this excludes the second tiles diagonal from your city itself.
3) Cities don't defend themselves at all, right? So, how full should I stuff my cities with defending units? Is one archer okay in the early game?
I try to have at least three archers early game as defense and then add or subtract depending on how much barbarian attention you get and whether the city itself is already a "second line" city(That is, not a front line city)
4) It seem like production can be queued, but if I click a unit, it automatically goes to the top. I can't drag and drop and there are no "move up" and "move down" arrows. Is there a convenient way to manage it?
There is a specific key combo to do this that you can find under "shortcuts" in the Civilopedia.
5) I automated some workers, but they completely ignored improving the iron near my cities, so I had to manually send them over to mine it. Is there a known reason for this hesitation?