1. Hi, you cannot plug a pair of Beolab to a line out. It need to be a variable level, like the headphone output from your TV.
However, I would recommand going through a Beosound.
2. Yes, they all have a AUX IN, so you can connect the line out (this time) from your TV to the Aux IN of your BS. Regarding 2.1 or 5.1 the answer in no... the BS are stereo only.
3. Yes, that is the point.
4. Yes, absolutely, you would need the 3000 or 3200, connect a Masterlink cable from it to the other room. In the other room, you can install a module called a Beolink active, to which you connect an IR eye and a pair of Beolab speakers. Otherwise, you can install a Beolink passive module and connect a pair of "normal" speaker.
5. As the only AUX of the BS will be taken by the TV, you will not be able to connect the ipod to the BS. You would have to connect it as a TV source, and call it from the TV.