Regarding your questions:

1) Unlike the Tiger version of Front Row, the Leopard and Snow Leopard versions of Front Row exclusively access the display. No other application can put windows or menus on top of it. Front Row needs to be quit before any application can show any window or menu. In contrast, EyeTV doesn't do anything such and doesn't have such issues.

2) This sounds like essentially an EyeTV/Digital Audio Out topic, so I'm afraid I can't help much here. You could, however, most likely work around this issue by creating an action with an AppleScript snippet that performs this action for you and place that action as an item in your Remote Buddy menu. Something else worth checking in that context is which audio device you've selected in EyeTV Prefs > Audio for audio out. IIRC selecting "System Audio Out" should avoid exclusive access issues like these. I can't really tell because as of yet I don't own any digital audio equipment.

3) This option is only available to kiosk applications for now. Please file a support inquiry if you need control over this feature and I'll provide you with the necessary information.

Best regards, 
Felix Schwarz

P.S.: Danke - und ebenso einen guten Rutsch in neue Jahr :-)