I've been making up stuff for Alexander as I go along, so I won't argue if you do the same. What did you have in mind in terms of powers for her? Regarding Christian theology, I'm thinking of her bringing locust plagues, famine, earthquakes (done lol) and other natural disasters, disease, etc... But much of that would seem a bit overkill right now. Maybe if (and only if!) Alexander escapes and it ticks her off, haha...

Perhaps you can meet half way between her being serious and toying the man? Toy with him just enough to get that real sense of being otherworldly, say just enough to be mysterious. I don't know if I'm making any sense.

Hope this is at least a little helpful?