I) Red Box = base is uncapturable
(Minor glitch: Sometimes it may appear as if all bases on your map have that box and are uncapturable. It's just a small software glitch and doesn't change capturability (?) at all)
II) "Base under attack" is triggered (and base is starts to flash) when an enemy has entered the warnign range. Which has approximately the same distance as the radar ring in case of airplanes. For GV's it's much smaller. I don't have the exact distance in my memory, but it's somewhat like 5K yards.
(Big glitch: If you log on and a base is already under attack, you won't see it flash on map)