OK, I'm biased, but whatever - awesome idea. Utterly awesome. Details might need some work, though, that's why it's just an idea at this point. It's a bit like the pet from Black & White but as a companion. Also, it distantly reminds me of Fable. Keep the idea, try to implement it.
Now as for your questions
1: Who cares? Oh...right. Well, leave it open for interpretation. It could be that dude created a new body for himself, or maybe it's a spirit (or whatever have you) which just haves odd thinking patterns. Besides, what differentiates a child from an adult, really? If she learns and acts as an adult, is she? What about other adults, then, just because they have a couple of decades experience, are they better at being adults than her? people will pick on it. Let them. Make them. If you reach the point where massive threads of discussion surround the matter, I'll count it as a success.
2: Well, it could be, depending on the presentation. It doesn't have to be, though. If you're worried you can't write it "serious" enough, scale back the TnA.
3: Hmm. I'd rather have difference. Otherwise, she'll just end up being another Liara. I suppose you can base gender on what preference has the player shown so far. Also, good point to explore - the PC gets to like one NPC and suddenly a rival comes up.