In Sumerian and Babylonian thought, the netherworld had no "levels" as such. Although Ea's subterranean realm of Apsu or fresh water was often conceived as one "level" above the underworld, it was not an abode of the dead. Neither can the netherworld be compared to the medieval Christian conception of Hell as a place of punishment and torture for the wicked. On the contrary, it was the common destination of all humans.
The netherworld was usually portrayed as a dry, dusty subterranean abode where the dead exist in a kind of shadowy half-life. However, the level of comfort and status the deceased enjoyed varied considerably. According to the Sumerian poem, Bilgamesh (=Gilgamesh) and the Netherworld, those with more sons enjoy better conditions. Additionally, the manner of death and the measure of respect displayed in life towards parents and gods are influential factors.
In the Sumerian poem, the death of Bilgamesh, the great gods decide that, even though he is part divine, Gilgamesh cannot be granted immortality. As compensation, after death he will become the governor of the netherworld. Perhaps this very old Gilgamesh tradition goes part way towards answering your question about the status of the king in the realm of the dead.