Assuming we have a nominal definition (and even this will often have to change) he first principle of understanding Hell is to get clear on its duration.
For our purposes, a duration is any way in which a variable being can relate to a more uniform measure.
The easiest duration for us to understand is time, where both substances and actions are measured by a more uniform substance (like a star) and a more uniform action (like the rotation or orbit of the earth.)
Eternity is the duration of unchanging an unchanging substance and an invariant intellectual action, and such an action would have to know all being at once. This is the duration of the blessed, who have this vision relative to the more uniform measure of God’s knowledge of himself.
Aeviternity is the duration of an unchanging substance but, because it has does not have the beatific vision it has more than one thought. Those with more thoughts are measured by the one with fewest.
The duration of Hell is aeviternity and not time, neither is Hell eternal as a duration.
1.) Punishments in time are proportionate to the time of the punishment, so a punishment for an unending time would exceed proportion to any finite fault. But aeviternity is not an unending time.
2a.) Grace is in the essence of the being receiving it. The essence of what is in eternity is unchanging, and so what occurs in time must be able to occur as it were in a moment. Now either an act of turning to or turning away from God can happen in a moment, but not a turning away and then a turning toward. Repentance, however, requires both acts, so repentance is not possible in aeviternity. God does not save those in the aevum because he can’t, and he can’t because it involves contradiction. If we’re going to convert, it has to happen now; and if an angel falls, that was his last chance.
2b.) Those in Hell have free choice, and a being with free choice can always choose a salvific act of charity, but any act of charity presupposes grace. So a damned being has free choice and cannot make a salvific act of charity.
3.) Though our lazy understanding of eternity makes it an unending time, there is no unending time. Time began with the creation of the cosmos and it will end after the eschaton. Even after the general resurrection the body will be proportioned to either the participated eternity of the blessed or the aeviternity of the damned. The temporal itself is finite, and even if not in its terminus a quo it is in its eschatological terminus ad quem.
4.) The aevum is intrinsically permanent, unlike time which is intrinsically impermanent. An everlasting time would have to be imposed from outside by a continual divine action; an everlasting aevum is simply the duration of the things existing there. One isn’t sentenced to a permanent punishment in the aevum – he is a permanent being with a punishment.
5.) One complicating factor is that the damned are bound to a (somehow) temporal fire. They aren’t bound in a manner that makes them a temporal essence in the way that the soul and body are one essence in a person, but in an extrinsic manner appropriate to the punishment of a free being.