So I got my Fire TV. It has some CEC support because it shows up as a source to my TV and the TV and receiver correctly switch to it. My TV remote, however, does not control the Fire TV. Given that the HDMI hardware supports CEC, I think this was their choice and one that they hopefully will change with a software update.

This is the thing I want to know the most. So I bought one and will probably return it if it doesn't.