We can use the Sun as a focusing lense - need to place the antenna at 500+ AU behind the Sun on the line of the desired communication.

>On the other hand I can't understand the propulsion mechanism.

Yes, i also think the laser propulsion isn't the one to go, at least with the current tech. With current tech my bet would be on ion drive https://news.ycombinator.com/item?id=38445404