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The solid materials collided with each other and accreted to form gradually larger bodies, until the Solar System's four terrestrial planets (Mercury, Venus, Earth, and Mars) were formed. -
This happens before the planetary cooldown, a few thousand years after the accretion. The formation of the moon happens because the planet Theia collided with Earth, and they create a new mass and spinning off became the moon.
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After Earth was formed into a planet, the temperature was really high that no organism could live in it. So after billions of years of the planetary cooling, the water started to appear on the planet.
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During the Heavy Bombardment, there are millions of masses hitting the proto-Earth. Those masses make Earth grow bigger and bigger, the bombardment stopped in a few hundred million years after.
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The core formation happened after the planetary cooldown, all the heat went to the center of the planet.
