What is Hell?
What are Sheol / Hades / Prison / Lake of Fire / Outer Darkness?
Allow me to restate the passages you have provided using the NASB-95 translation. I believe what’s crucial to recognize throughout this discussion is context.
I. My rendering of Psalm 16 reads:
Psalm 16:10: “For You will not abandon my soul to Sheol; Nor will You allow Your Holy One to undergo decay.”
II. The passages from Luke 16 read:
Luke 16:22-23: “Now the poor man died and was carried away by the angels to Abraham’s bosom; and the rich man also died and was buried. In Hades he lifted up his eyes, being in torment, and saw Abraham far away and Lazarus in his bosom.”
My version does not read “Hell” –- nor should it. This must be understood as “Hades,” which will make sense in a few moments.
III. The reference in 1 Peter 3 from the NASB reads:
1 Peter 3:19-20: “[In which also Christ] went and made proclamation to the spirits now in prison, who once were disobedient, when the patience of God kept waiting in the days of Noah, during the construction of the ark, in which a few, that is, eight persons, were brought safely through the water.”
In the above passages, we must understand what is being said in context. There is no way we can decipher the passages if we do not do this. When we do (momentarily), we will see that 1 Peter 3 cannot be referring to Hell.
IV. The passages cited from Revelation are highly symbolic:
Revelation 20:12-14: “And I saw the dead, the great and the small, standing before the throne, and books were opened; and another book was opened, which is the book of life; and the dead were judged from the things which were written in the books, according to their deeds.
And the sea gave up the dead which were in it, and death and Hades gave up the dead which were in them; and they were judged, every one of them according to their deeds. Then death and Hades were thrown into the lake of fire.”
It would take another post to decipher much of what is written here. Suffice it to say that the "books to be opened" are the record of our lives, our consciences; we are either written in the Book of Life at death or we are not; notice that the (spiritually) dead are judged, not the saints; death and Hades (not eternal) is to be - future tense - thrown into Hell (the Lake of Fire).
V. Finally, the passage from Matthew reads:
Matthew 8:12: “[But] the sons of the kingdom will be cast out into the outer darkness; in that place there will be weeping and gnashing of teeth.”
1. Do sheol, hades, inferos, phulaké, limnēn tou pyros, and skotos to exōteron refer to the same thing? If not, what is their relationship?
“hades”, “phulaké”: First, Hades is understood the temporary abode of the lost as we see in Lk. 16:19ff. This will be reinforced as we continue, but note the rich man has yet to be judged. He is languishing in torment prior to his final, eternal destination: Hell. He is hardly alone.
“sheol,” “gehenna”: While you didn’t mention the word “gehenna,” as I recall both of these words are understood by many to refer to “Hell.” This is the final abode of all the wicked following judgment, not before.
“limnēn tou pyros”: I would suggest that the Lake of Fire is the same as Hell. In Matthew 25 we read:
Matthew 25:41: “[Then the King] will also say to those on His left, ‘Depart from Me, accursed ones, into the eternal fire (“sheol,” “gehenna”) which has been prepared for the devil and his angels.”
This is referring to an eternal fire, not the temporary prison we read about in both Luke 16, 1 Peter 3, and elsewhere.
“skotos to exōteron”: I’m unfamiliar with the term “inferos,” but “skotos to exōteron” could be referring to either place of doom since, irrespective of whether one is consigned to Hades or Hell, they are both very much “outer darkness.” I propose the only distinction is that Hades is temporal while Hell is eternal.
2a. Is what is being described “A place” (from 1 Peter 3 he went there; spirits were in prison)
From the passage in 1 Peter 3, we should understand that verses 19 and 20 are relating a story about those who are now in prison (“phulaké”) at the time Peter wrote his Letter. There is a timeless truth about the Spirit of Christ to be recognized in these verses if we can spot it. Allow me to paraphrase:
1 Peter 3:19-20: “[In which Christ] went [in the Spirit] and made proclamation [through Noah: 1 Peter 1:11] to the spirits [people of the pre-Flood era that are] now [at the time of Peter’s writing, finally] in prison, who once were disobedient [before the Flood], when the patience of God [through Noah] kept waiting in the days of Noah [Noah preached for 100 years], during the construction of the ark, in which a few, that is, eight persons, were brought safely through the water.”
This entire narrative is speaking of the spirits of those who were once human, now in the prison of Hades as Peter writes. Hades must be temporal because it now exists (1 Pet. 3) – unlike Hell.
2b. Is it a state of being (from Luke 16 the rich man was in torments)
Hardly. The figure of Abraham is most likely God. The Jews considered Abraham their father (cf. Jn. 8). In the N/T, God is our Father. Nonetheless, the narrative contains parabolic elements; note that the rich man possesses certain spiritual/physical? characteristics that demonstrate at least an awareness of sight, touch, and hearing. No, the rich man is in the temporal realm of Hades – a prison where those from 1 Peter 3 are also languishing.
2c. I am afraid I can discern nothing else.
3a. What is meant by hell delivering up the dead (from Rev. 20)?
Here, my version (NAS) states:
Revelation 20:13: “And the sea gave up the dead which were in it, and death and Hades gave up the dead which were in them; and they were judged”
I propose that the correct interpretation here is Hades. That is because no one will be “given up” from Hell, it is permanent.
3b. Do some or all of those who leave return?
Hell is a state of permanence. It is unclear to what you are referring, but no one will ever “return” either from Hades or Hell. Each one of us has been given a lifetime to decide our fate; we are alone in doing so. In Hebrews, we read:
Hebrews 9:27: “And inasmuch as it is appointed for men to die once and after this comes judgment…”
There is no turning back from these horrific destinations. I have inserted a graphic that helps me visualize Hades (vs. paradise). I have omitted Hell since I think we can get that picture based on this one:
I hope I have not overlooked some of your questions: I could have. I did my best to parse all of it to provide what I see as reasonable explanations to each of your points based on the evidence and context.
(Ah, I see you added “Gehenna” to your list at the end.)