gravity - If an asteroid twice the size of Earth passed super close would half of the Earth be pulled towards it?

The Earth wouldn't simply split in half, it would be pulled towards the asteroid as a whole. To simplify matters, let's assume that the mass is equal to twice that of Earth (size alone is not enough, you must also consider density). You can then use Newton's law of gravitational attraction for the calculations:

$$F=G frac{m_1m_2}{r^2}$$

$G$ is a constant, $r$ is half the distance between the moon and Earth, $m_1$ is the mass of Earth, $m_2$ is twice that. The gravitational force would be about $1.3 times 10^{29} text{ N}$. In comparison, The gravitational attraction between Earth and the moon is about $2.0 times 10^{26} text{ N}$. Which means that the attraction Earth-meteorite will be 2000 times larger than Earth-Moon. The Earth will speed rapidly toward the asteroid and crash into it. During that flight Earth indeed is to be expected to have gravity fluctuations and probably lose major parts of its atmosphere. However it is unlikely that Earth, being a telluric planet (made of rock and metal) would subdue major deformation. After all, Jupiter's moons are round, even though they are in much more extreme conditions.

You would however need to consider the velocity of the meteorite for any more precise estimations. The speed and the trajectory count. An object that passes faster would tear the Earth out of its orbit but it would continue moving, whilst if you just place that meteorite between Earth and Moon, Earth (and Moon) would simply fall on a perpendicular trajectory.