Can the FX7, unlike the FX1, display on the viewfinder and LCD simultaneously while you're shooting?

Yes, it can.

Thanks, Piotr.

Is there a special option? Mine turns off one or the other depending if the LCD is open or not.

Yes, you have to choose the option, but you can have both VF and LCD active at the same time, and it's a handy feature! I like to switch back and forth while shooting, so I was glad to see this capability.