Twilight could possibly love animals, but I doubt she loves animals as much as Fluttershy does. She might like them alot, but it was proven in "Winter Wrap Up" that she just isn't good with animals like Fluttershy is. I think this is because she might not have as much experience as Fluttershy does, and is always reading books. And yeah, she probably knows stuff like calculus. She is insanely smart after all.
As for Rarity, I agree that she does have share a few of Twilights traits when it comes it comes to both being OCD, for reasons that don't need to be explained. But I would say that Rarity is more OCD than Twilight, when it comes to dresses. But I wouldn't go as far to say that she knows calculus, it only takes basic math to make dresses. As they are both Unicorns, they share a few of the same traits.