I have some goofy ideas for stuff I wanna try, but I need to know what my options are for communicating information to the player. Is there any place in the sdk I can browse the available functions in CyInterface? It appears there is nothing in the SDK that's actually called CyInterface.

Many classes are not part of the SDK.
Take a look here: http://civilization4.net/files/modding/PythonAPI/
Some classes are marked as not in SDK.

Matze