1. You should use that option, yes.
2. Not 100% sure, haven’t tested that – but I’d say, yes it switches on with the incoming signal.
3. (If I understand your question right) sure, that is how it is supposed to work – but you will need an adapter PL/RJ45 to PL/DIN.
Yes, you can set the Beolab 11 to “Line” mode via the selector switch and it will turn on and off automatically when the sound plays. Please use this cable to link the Beolab 11 to an amplifier or receiver with volume controlled RCA pre-out sockets (I apologise that this link will only work for UK visitors at the moment):-