# Wasn't Earth a magma ocean before core-mantle differentiation?

I've always thought that the process of planetary accretion was energetic enough to keep the proto-Earth entirely molten, and the subsequent evolution of the planet (the formation of the crust, etc...) was simply centered on its cooling by gradual liberation of the trapped heat (from those planetesimal collisions and radioactive decay).

But recently I've read that there was a particular event called core-mantle differentiation, or the "Iron Catastrophe", that occurred after the formation of Earth (and before he formation of the Moon), which transformed "an undifferentiated mass of solid rock" into a magma ocean.

• Does this means that previous to the core-mantle differentiation, the Earth had a primitive solid surface? That this surface was turned into a magma ocean because of the feedback loop of core-mantle differentiation and then, when things cooled down, a second generation crust formed (which was later destroyed by Theia's giant impact)?
• Does the process of rapid accretion of planetary embryos trapped so little heat inside Earth that the additional heat from radioactive decay was needed to build up enough temperature to melt the iron afterwards? Does this mean that each of the planetesimal impacts melted only part of the embryo (I guess that if they could yield enough energy to melt the entire object they would have made possible Earth's differentiation way before the core-mantle differentiation)? Does these impacts were infrequent enough that the embryo could have solidified and cooled down before the next accreting event? How can accretion form an undifferentiated Earth before the core-mantle differentiation at all?
• If a planet is accreted only from non-radioactive material, should we expect an Earth-size planet with no differentiated interior? Since radioactive decay was apparently needed for the "Iron Catastrophe".