Help! Resolution Settings

[JJ777]

I have a Sony KDF-42WE655 HDTV (1386 x 788) and am confused about 1080i, vs 720p vs dvd signals vs broadcast signals, etc.

I have done a bit of research and still am a little confused about what resolution is actually being displayed on my TV.

First, I have a PS3 set to 1080i output. When I play my blu-ray movies are they being displayed in 1080i or being down processed to 788p?

Also, I receive high-def broadcast TV signals. Some stations state they are in 720p (Fox, ABC) and others 1080i (NBC, CBS, PBS). I do notice that the 1080i stations look sharper, but there is some movement/ghosting effects (probably due to the compressed signals). Question: when I receive the 1080i broadcast signal is my TV displaying 1080i or again, down converting to 788P? It seems like if it was down converting than it would be progressive and I would not get any movement/ghosting (as I certainly do not when I watch the 720p station). It seems like the TV is displaying 1080i.

I have seen some info in the forums, but still am not sure.

Please help clarify.
Thanks
Josh