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Thanks for asking.
1) The simpliest way would probably be to add a simple custom action
that sends Apple + W to EyeTV. Which of course assumes that the Live
TV window is the currently focused window of EyeTV. The more complex
way is to write an AppleScript that goes through the list of EyeTV's
windows and identifies and closes the Live TV window. That
AppleScript, too, would have to be added as a custom action at/via RB
Prefs > Mapping > EyeTV > Select "Custom actions.." in the popup.
If you need step by step instructions, please consult the Online
Help's "How do I.." area.
2) Again, you can achieve this via a custom action, with f.ex. this
AppleScript:
tell application "EyeTV"
activate
set full screen to true
end tell
In the custom action editor, you'd want to check the checkbox for this
action to make it global. You can then put it anywhere in the menu and
also map it to any button of your remote in any mapping table.
Best regards,
Felix Schwarz