We don't see very many shots showing the outside at the time, but BD did give the command to evacuate. If there weren't ships, then it would be kind of silly for him to give the command.
When ADAM activated there wasn't any indication that they weren't aware of what it was. And EVE's job wasn't to protect the entire Megazone, but to choose who should be allowed to return to Earth. This is why all of Shogo's friends who were scattered all over the city and in pretty bad shape all made it, but nobody else did. EVE specifically saved them. She was sort of a filter to make sure only humans who weren't going to screw up the Earth again would be able to land.
He does fly off. Which is odd if he had just given up and is willing to die. If he wanted to die, he could have just stayed there and been disentigrated along with the rest of the Megazone.
You mean besides the other seven planets and millions of planetoids that make up the solar system?
Whether BD is alive or not is an unknown, but I think the creators of the show definitely left the implication that he was not destroyed along with the Megazone.