Just purchsed GSX today. Installed it, and got the same two error messages that the original poster saw "Problem downloading AFD scenery list!" and "Problem downloading Couatl plugins list!"
Booted up FSX, loaded a flight at a default airport, KLMT, and GSX showed up and worked as advertised.
In mid flight, FSX crashed on me.
Then I tried the flight again a few hours ago, and GSX would not show up. It was listed under the Couatl for key mapping, I then changed the key map, something I wanted to do anyway, but still no luck.
Re-install GSX, same two error messages show up (my computer is connected to the internet by the way), and GSX showed up (plane parked at your KLAS), and worked as advertised.