What is a good polygon count for characters on the iPhone? What is the platform capable of if there are only three characters on the screen at once, against a pre-rendered background?

It really depends on how many character you will have on the screen and how close/detailed you want them. As far as I know there is no hard limit on the number of polygons but of course the more you have the slower your game will run. I've found that I can render 8-9k textured tris without much issue but much more than that you will see your framerate drop to an unreasonable level.
For most of our games we have kept the character tris around the 500 range depending on how much we want to display on the screen.

I don't have any direct answer to you questions, but you might want to check out this thread:
http://forums.toucharcade.com/showthread.php?t=11825

=)

From the numbers I've seen posted about, it seems the iPhone can do approximately 400k per sec for static scenes and about 1/10 that for dynamic data. So I would estimate at a desired framerate of 30fps you can update ~2k per frame. Dividing by 3 you have about 300-500 polygons per character at 30fps. That should give u a range, but the best way to know for certain is to actually test this on the iPhone, be aware different generation of iPhone have different performance specs.

Good Luck!

-ddn