As far as what you have stated about Lina, I feel the same way, although I don't really know if I am able to judge the performance itself on it's own merits simply because Lina is Sweedish, and I am not. Believable, yes most definitely, but how much of that believablility (is that even a real word?) is because she is foreign. That aspect alone gives me an advantage over a Swede in my capability to not judge the acting because I have no idea what a 12 year old Swedish girl 'should' act like, let alone what a 250 year old 12 year old Swedish, vampire boy/girl should act like! In any case it doesn't really matter because the end result for me is that she simply was Eli.
I genuinely don't understand the 'I can't judge her performance because she's foreign' argument. By that logic, I -or anyone who isn't American- couldn't judge the performances of American actors. By that logic, only the people from the country a movie is made in are able to judge the performances of its actors. Maybe it's because I'm from a small European country and almost exclusively watch foreign movies (mostly American of course), but I don't see how an actor speaking a different language and being from a different country matters for the performance. It seems to me emotions are universal: sad and lonely in Sweden isn't going to look wildly different from sad and lonely in America. You can feel if they're authentic without knowing everything about their culture, or speaking the language. Me not speaking Swedish doesn't make me less affected by Lina's facial expressions, her body language and the way she delivers her lines. (Although of course she was dubbed, so maybe that doesn't really apply here)
The only thing we can't judge are the lines themselves: if it sounds
authentic. But that may actually be an advantage sometimes: if it doesn't, we won't hear it, and it won't distract us.
So: I don't think you need to be too concerned with how a Swedish girl her age 'should' act like. Especially not with this particular character, since Eli is obviously not a regular girl. No one actually knows what a 12-year old child who's lived for hundreds of years would be like.
I'm almost afraid to say it, but I never did warm to Chloe. In some moments, she manages to convince me (the 'be me a little' scene) and I'm like: oh so she is a good actress! But most of the time when I see her in something, I don't see the character, I see her pretending to be that character. And she pretends really hard, and I don't doubt it she's really giving her career her everything, but often she can't make me believe in her. Sorry guys, that's just my personal opinion! That being said, I do think Abby was one of her better roles.