Well, with her mother being sent down to Earth, I would consider her a spy. Perhaps not specifically trained for fighting as soldiers are(being that she was being groomed to take her father's place), but they still wouldn't send her down to Earth without any fighting skills at all. I can see her having taught both Eve and Toni how to fight from a young age. 
As far as which would be the reason for him not trying to kill her instantly, I would probably go with her convincing or tricking him to not kill her. Because, to be honest, she would have a very similar mindset as Cae and would kill him if she disarmed him XD
I'm thinking I'm going to make Evelyn of similar mindset to the halfbloods in the old rp, in the fact that she will hate Lunairans. It is kind of ironic, being that she is half Lunairan and her mother was a full Lunairan, but after the invasion and her parents and brother being killed, she would view the Lunairans as evil and hate them. This also means hating herself for being part Lunairan. The reason that she hides her eyes. She hates her eye with a burning passion because it reminds her of the Lunairan blood that courses through her veins.