kieto, first of all, there were no other nodes out of Sol. The Delta Serpentis-Sol node is the only one. The other nodes shown in the command animations were an error, as was the line by Alpha One in the final monologue; one of the Volition people admitted as much. They had only ever planned to have one node. Kind of makes your evacuation impossible, doesn't it? And, as aldo said above, there's absolutely no way to evacuate billions of people at the drop of a hat. The final attack on the Lucifer truly was Sol's last hope.
As for the beam weapons, I can't remember the exact location, but I know it was mentioned somewhere in-game that they were reverse-engineered from the Shivans. It doesn't matter that the Lucifer's wreckage wound up in Sol; as I said above, the alliance had obtained detailed scans of the Lucifer; it also had the Ancients' data to work from. Obviously, that was enough for them to eventually create working beam cannons.