What is the ruling on the issue of eternal damnation in Hellfire, and in the case of non-eternity, what happens to those who were in it, given the authentic hadiths that mention categories of people who will not enter Paradise and others that indicate that the dwellers of Paradise and Hellfire will not die?

Two types of people enter the Fire: Believers, monotheists, whose evil deeds outweighed their good deeds. They remain therein for a time, then they are brought forth from it into Paradise by the grace of Allah. And disbelievers, who die upon their disbelief. They enter it, abiding therein forever, neither dying nor having their torment lightened. This meaning is frequently mentioned in the texts of revelation.