It should just work. At least in your apps it should. (Netflix, YouTube, Hulu, etc.) Google Cast is cross-platform. You just can't mirror from iOS.

There are apps to make AndroidTV into an Airplay receiver. I haven't tried any, so can't comment. You can cast from an iPhone the same the same way you can from an Android Tablet - just look for the cast symbol in the app you want to cast from.

If you meant cast the entire screen, no matter what's happening (a display mirror), you should edit you question to mention this and you might get some more specific answers.

All of the same apps on iOS that are on Android usually support casting. Netflix, YouTube, ESPN, etc all work the same. There is no pairing process for casting. You just have to be on the same network.