I haven't tried it myself but that's definitely an interesting test! That said I don't believe it to be possible, based on the error received but I've been wrong before. Perhaps someone from the community could weigh in to confirm?
2. Some TVs have "passthrough" for "external speakers" (which may be similar to headphones) when using HDMI as your input, however, you need to enable that option in the TV's audio menu. Have a look at your TV's audio menu. Note that if you change that to "external", the TV's internal speakers will likely be shut off and you'll need to revert to your previous settings for the TV speakers.