Fragments begin striking the Earth's surface minutes after the asteroid strikes the moon. No matter how violent the impact, pieces would take days to reach the Earth, where they would most likely spend still more days or months in low earth orbit.
The experts in the film continually refer to the asteroid as a brown dwarf, a remnant of a dead star. In fact, a brown dwarf is a body which, although very large, is still too small to ever actually ignite and become a star in the first place.
The plot hinges on the relatively small piece of the asteroid which remains embedded in the moon being of very high mass, due to its high density as a piece of a brown dwarf. In fact, the only reason the density of a brown dwarf is so high is because of the dwarf's large mass, which generates such a high gravitational field it compresses the mass. If a piece of it is removed from the gravitational field, it will expand until its density is that of normal matter, much as compressed air taken out of the tank no longer remains compressed.
In the beginning of the movie, people from America and Europe are watching the meteor shower at the same time. Not only is it not nighttime at the same time on both sides of the planet, but the moon would not be visible to both sides at the same time.
A fragment of a superdense "brown dwarf" star with a mass twice that of Earth crashes into the moon, which alters the moon's orbit. In reality, if a mass with twice the Earth's mass struck the Moon, the Moon would disintegrate in a cloud of molten droplets. The massive body would then continue on its way. In its passage at the distance of the Moon, its gravity would cause massive tides in Earth's oceans, inundating much of the land. At the same time, it would cause tidal forces in the Earth's crust and mantle that would probably cause the crust to fracture in so many places that magma from the mantle would erupt onto the surface and cover much of the Earth. Much of the water in the oceans would turn to steam. The escaping magma would release so much toxic gas (carbon dioxide, sulfur dioxide, etc.) that the atmosphere would be poisoned and the CO2 would cause a runaway greenhouse effect, raising the Earth's temperature hundreds of degrees. After 100,000 years or so, there might be enough cooling to allow atmospheric water vapor to fall as intensely acid rain incapable of supporting life and causing weathering which would remove so much CO2 from the atmosphere that it might precipitate a new Snowball Earth. -- If a fragment of a brown dwarf with twice the mass of Earth were CAREFULLY DEPOSITED on the Moon so that it did not destroy it, the mass asymmetry would cause wild variations in the Moon's rotation and orbit. More importantly, it would shift the center of mass of the Earth-Moon system from near the center of the Earth to near or even inside the Moon. Then the Earth would orbit around the Moon instead of vice versa. The shifts in angular momentum during the change might be severe enough to cause both the Earth and Moon to break up, leaving a cloud of fragments to orbit the sun. The fragments would then accrete around the brown dwarf fragment, and eventually form a single planet with the combined mass of the Earth and Moon. If any life had survived on any of the fragments (not likely), it would be single-celled life that would either not survive or would begin the whole process of evolution from single-celled organisms all over again. And this time, there might not be any evolution to multicellular life.