Does python have a method for getting a list of the group(s) an object belongs to?
As far as I know, the groups are only available in Blender proper and not the game engine. If you want to use groups in BGE then I think you’ll need to write a script to write a file defining what object belongs to which group that can be read from the game engine and then read that file in some kind of init script and store the information from there (like in a dictionary or a list of lists).
I believe that linked groups are usable in BGE, but I am not sure of the limitations of these.
Edit: If you look at the Group.Group part of the API here then you should find how to access groups via Python.
On the subject of parts of the Blender API that go Group.Group or Scene.Scene how do you access the second Scene? I always get “module has no attribute named Scene”
GameLogic.getSceneList()
http://www.blender.org/documentation/249PythonDoc/GE/GameLogic-module.html#getSceneList