Unfortunately, I don't think there is a way to embed a flash player instance directly into Objective-C like there is in C#.
Windows relies on using the ActiveX control embedded into a C# container, but there is no equivalent to ActiveX on Mac OS X.

Then next best thing would be to embed and instance of WebKit, and then have that display the Flash. I'm not sure, however, if you can then communicate with the rest of a Cocoa application from the Flash embedded in webkit. Maybe through ExternalInterface going through WebKit, and possibly there is something in the API that lets you inspect properties within the WebKit instance.

I'm not sure, but it's not as simple (and that's not saying that it was easy on Windows).

Presumably it is possible, as companies like multidmedia have pulled it off with Zinc. But they are also licensing the Flash player from Adobe so have and are basically building their own entire 'shell' around a flash player instance.