The second death is where the first Death and Hades are thrown into. The first death was physical, separating the soul from the body. It was, of course, a result of the Fall. However, that also resulted in man's separation and alienation from God. Christ's death and resurrection provided the means for reconciliation and relationship with God. The second death, then, could very well be where body and soul aren't annihilated, but separated from God for eternity.
That going to hell for eternity is "for even minor offenses they committed in their short lifetime" is not accurate. They are judged both on works and on whether or not their name is in the book of life (Rev 20:12, 15), and so go to hell for rejecting Christ and living in rebellion to God. The idea that God "is going to torture people eternally" is also not correct and seems to be typically used as rhetoric to dismiss the idea of people in hell for eternity. It is my opinion that there is a lack of understanding about what happens in hell. Consider:
Luk 12:43 Blessed is that servant whom his master will find so doing when he comes.
Luk 12:44 Truly, I say to you, he will set him over all his possessions.
Luk 12:45 But if that servant says to himself, ‘My master is delayed in coming,’ and begins to beat the male and female servants, and to eat and drink and get drunk,
Luk 12:46 the master of that servant will come on a day when he does not expect him and at an hour he does not know, and
will cut him in pieces and put him with the unfaithful.
Luk 12:47 And that servant who knew his master's will but did not get ready or act according to his will,
will receive a severe beating.
Luk 12:48 But the one who did not know, and did what deserved a beating,
will receive a light beating. Everyone to whom much was given, of him much will be required, and from him to whom they entrusted much, they will demand the more. (ESV)
I do not agree with the seemingly common idea that there is going to be eternal physical torment in the form of some sort of torture that causes pain. It seems that while the Bible teaches the punishment of being in hell is eternal, any physical punishment is temporary, although temporary compared to eternity could still be a very long time,
and varies in severity from person to person. This is consistent with Paul stating in
1 Cor. 3:12-15 that believers will receive different levels of rewards. Different levels of punishment for unbelievers, different levels of reward for believers.
Therefore, any concept of an eternal hell for unbelievers needs to take into account that there seems to be limited physical punishment. Torment can be psychological, based on regret, depression, aloneness and separation, etc. Any "eternal torment" then, would likely be mental anguish over what is instead of what could have and should have been. Would it not be absolutely gut-wrenching to be in hell, with all physical punishment having ceased, and realize exactly where you went wrong and why, how you justified sin and unbelief, and to know what you have missed out on, for eternity?
I think at the judgement seat all things will become clear--the clear evidence for the existence of God, the pursuit by God, and love of God, all rejected for the purpose of serving self and seeking pleasure--and the unbeliever will know that they got what they deserved.
One problem with annihilationism, which it seems you believe, is that it is unjust. Those very same people that you say committed minor offenses suffer the same punishment as people like Hitler and Stalin. In order for it to be just, there must be punishment that fits the offense, don't you agree? When does that happen?
Another thing to consider, taken from an article in The Apologetics Study Bible, written by J. P. Moreland, and titled "Does the Bible Teach Annihilationism?":
"Does the Bible teach that the unsaved will suffer in hell for only a time and then be annihilated? Some argue from Scripture that the flames in hell are literal and point out the flames destroy whatever they burn. Further, they claim that infinitely long punishment is disproportionate to a finite life of sin. Thus extinction is morally preferable to everlasting punishment.
The scriptural argument is weak. Clear texts whose explicit intent is to teach the extent of the afterlife overtly compare the everlasting conscious life of the saved and the unsaved (Dn 12:2; Mt 25:41,46). Moreover, the flames in hell are most likely figures of speech for judgment (cp. Heb 12:29; 2 Th 1:8). Otherwise, contradictions about hell are apparent (for example, it is dark despite being filled with flames).
The moral argument fails as well. For one thing, the severity of a crime is not a function of the time it takes to commit it. Thus rejection of the mercy of an infinite God could appropriately warrant an unending, conscious separation from God. Further, everlasting hell is morally superior to annihilation. That becomes evident from the following consideration.
Regarding the end of life, sanctity-of-life advocates reject active euthanasia (the intentional killing of a patient), while the quality-of-life advocates embrace it. In the sanctity-of-life view, one gets one's value, not from the quality of one's life, but from the sheer fact that one exists in God's image. The quality-of-life advocates see the value of human life in its quality; life is not inherently valuable. Thus the sanctity-of-life position has a higher, not a lower, moral regard for the dignity of human life.
The traditional and annihilationist views about hell are expressions, respectively, of the sanctity-of-life and quality-of-life ethical standpoints. After all, the grounds that God would have for annihilating someone would be the low quality of life in hell. If a person will not receive salvation, and if God will not extinguish one made in His image because He values life, then God's alternative is quarantine, and hell is certainly that. Thus the tradition view, being a sanctity-of-life and not a quality-of-life position, is morally superior to annihilationism." (p. 1292)
I think that is a very strong argument.