Short answers, pulled from the story.
The Duat is a dark subterranean realm where the sun god Ra travels during the night. This landscape contains twelve guarded gates that mark each hour of the night and serves as an underworld for both mortals and gods.
Anubis guides the soul of Hunefer into the judgment hall around 1275 BCE. He places the heart of the deceased upon one side of a scale while Thoth records the verdict with his stylus and tablet nearby.
Ammit waits near the scales ready to devour any heart heavier than the feather of Maat representing truth and justice. If the heart fails the test it is rejected and eaten forever, but those who pass travel onward to Aaru.
Papyrus copies date to the 19th Dynasty around 1275 BCE. The Papyrus of Hunefer shows Anubis weighing a heart against Maat's feather and the Papyrus of Ani depicts the Weighing of the Heart ritual clearly.
Absolute punishment means denial of existence rather than fiery torment for those who fail the judgment. Those who pass the ritual travel onward to Aaru where eternal spring ensures crops grow without suffering for the virtuous dead.