If Edward seems a bit ruthless right now, I'll just leave a quick explanation in case anyone's curious: 

He doesn't know Bea is just a child. All he's aware of is that she's an eldritch, nothing else. And given the mercurial nature of a lot of them, he's not going to take any chances; on the other hand, he's not going to off her immediately because he's aware that some Eldritch are actually beneficial to humans given the proper circumstances. The key will allow him to ascertain whether those circumstances are in place, which is also why he's asking Bea those questions.

I lied that wasn't really a quick explanation I'm sorry :v