I need to film the event and at the same time transmit the signal to be displayed on big screen lcd tv - what would be max length of the component cable I can use - I don't have any signal amplifiers.

Depends on the kind of cables you use. If you plan on using RCA connectors, I'd say, "not far". I did this with a set of BNC cables coming off the component connector on the camera and ran the cables over 100ft.

I displayed a 4:3 center cut on the display while recording a 16:9 image. Because of circumstances at the time, I had to record HDV signal to my firestore. Couldn't be helped at the time.