I suspect these are really old posts - I don't remember the term "communication lines" being used much, and we haven't discussed communication for ages (other than to answer an occasional question).
The green lines I see on my galactic map means that the two systems are connected by a jump point. If they're thick and orange (?IIRC), then that means that there's a jump gate on both sides of the jump point, defining a sub-network that the civies will use for trade.
All communications in Aurora are role played, i.e. house rules. I think Steve's rules are that all comms (and sensor info) within a system are instantaneous (FTL) due to some weird TN effect, and that anything at a jump point that allows transit (jump gate or jump ship) can propagate the information to the next system. My personal rules are that you actually have to have a ship stationed at the jump point that can carry the message across (i.e. the jump gate won't act as a com relay), but I abstract away the details of the ship jumping over and back - I just assume it does so.
On the "ars" message - are you using any sort of "send message" functionality where a text box pops up for you to type into? At present you can give a TF an order to send a message when it gets to a location. In SA (Starfire Assistant), you could "send" a message (as a reminder) with a delay of N turns - this let you mimic message propagation time delay. What you're describing sounds a bit like the latter, but I thought Steve took that out ages ago. And the "ars" part is totally unfamiliar. Maybe you could post a screen shot here the next time it comes up - there's an "upload attachment" tab below the pane when you're typing a message.
John
