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From what I can gather from what you are saying is that within Islam there are gradients of sin, some worst than others. By this reasoning if you commit a crime against another and they take revenge then both are forgiven. One balances out the other in Allah’s eyes.
If you are a murderer but the family of the deceased is well compensated by you or you are murdered yourself then the slate is wiped clean?
I dont think I understood you completely so forgive my not so somplete answer. If you dont get my answer then Ill try to explain more ok?

The first part is right. That within Islam there are gradients of sin meaning some sins are worse than others. For example of you kill someone that is of the worst sins i.e the greatest level of sins they are what we call in Arabic "Al Kaba'ir" meaning "the big ones". And then you have normal sins which we almost all do involentarely day to day. When you get out in the street and someone almost crashes in your car or so on and you shout at him or say between yourself hes stupid or something like that. So you have big sins, killing, also being a false witness, drinking intoxicants, adultry, slandering someones origin (saying he comes from the tribe of so and so mine is better. Or hes African Im American Im better and so on) and several others.
You said "if you commit a crime against another and they take revenge then both are forgiven". I dont understand what you mean exactly. But of course you're not allowed to take revenge for yourself, if someone kills your friend you cant just go and kill them you have to go to the authorities.
Murdering yourself i.e suicide isnt allowed under any conditions be it suicide bombings or you putting a bullet to your head out of depression.
On judgment day, we believe that, as I said every group of people who had problems or anything like that will be judged, meaning that God judge who was right and who was wrong. If a person slanders you in this life and you dont slander him back come judgment day you will take from his good deeds since he slandered you. Or, if he has no good deeds he will take from your bad deeds. That doesnt mean that God wont forgive him, it just means that you will either take his good deeds or he will take your bad deeds and they will be in his slaight. After everyone has been judged, one by one every person, you, me, every single person, will enter a place and he will be one on one alone with God. His deeds, the good ones and the bad ones will be put on a (I cant remeber the word for it. You know the thing which you balance out things with?) His good deeds will be put on one side and his bad ones will be put on another side. If his good deeds are more than he will enter heaven. His bad deeds will either be forgiven and the person he did those bad deeds against be rewarded or the person who had the bad deeds done against will not want to be rewarded but will ask that that person will be punished. If so, God will show him a very nice place in paradise and he will say my God to whom is this place ? To which prophet is it! And God will tell him this for you if you forgive your brother. Most likely he will forgive his brother because the place he will see is astonishing the very least so he wouldnt care about the man who had done bad against him to be punished. In that way, the bad doer will be forgiven and the guy who had the bad thing dont to him will also get his right and justice by being awarded. If someone doesnt want to forgive someone (this barely will happen) then the bad doer will be punished only for a certain period of time until he has been cleaned of this sin and then he will enter heaven.
You see judgment day itself, without us being punished for our sins, is very hard. Every single person every single son and daughter of Adam will be standing on a huge wight land, all of us, and we would all wait until we will be called so we will go and be judged. And we will be thirsty and hungry and the heat will be tormenting us. So the waiting itself until you get judged is torment so in that itself also justice is being done. To the bad doers, the more bad deeds you have done, the more the waiting will seem like a long time. To some, it will seem as if he's waiting 50,000 years. To others it will only seem as if theyve just prayed (the two raka prayer) and finished. The two raka prayer is the shortest prayer for the Muslims its the one in dawn.
To give you the details of judgment day and how we will be judged according to the Muslims id have to summarize hundreds of pages. But there are books which are strictly dedicated to this matter. How you will be judged. What will happen to you in the grave. How does your soul depart from your body. Almost every single detail.
This is a chapter from the Quran called al Qiyama (the rising of the dead or the Ressurection) its chapter 75:
In the name of Allah, the Compassionate, the Merciful. Nay, I swear by the Day of Resurrection;
Nay, I swear by the accusing soul (that this Scripture is true).
Thinketh man that We shall not assemble his bones?
Nay, We are able to put together in perfect order the very tips of his fingers.
But man wishes to do wrong (even) in the time in front of him.
He asketh: When will be this Day of Resurrection?
At length, when the sight is dazed,
And the moon is buried in darkness.
And the sun and moon are joined together,-
On that day man will cry: Whither to flee!
Alas! No refuge!
Before thy Lord (alone), that Day will be the place of rest.
That Day will Man be told (all) that he put forward, and all that he put back.
Nay, man will be evidence against himself,
Even though he were to put up his excuses.
Move not thy tongue concerning the (Qur'an) to make haste therewith.
It is for Us to collect it and to promulgate it:
But when We have promulgated it, follow thou its recital (as promulgated):
Nay more, it is for Us to explain it (and make it clear):
Nay, (ye men!) but ye love the fleeting life,
And neglect the Hereafter.
Some faces, that Day, will beam (in brightness and beauty);-
Looking towards their Lord;
And some faces, that Day, will be sad and dismal,
In the thought that some back-breaking calamity was about to be inflicted on them;
Yea, when (the soul) reaches to the collar-bone (in its exit),
And there will be a cry, "Who is a magician (to restore him)?"
And he knoweth that it is the parting;
And agony is heaped on agony;
Unto thy Lord that day will be the driving.
So he gave nothing in charity, nor did he pray!-
But on the contrary, he rejected Truth and turned away!
Then did he stalk to his family in full conceit!
Woe to thee, (O men!), yea, woe!
Again, Woe to thee, (O men!), yea, woe!
Does man think that he will be left uncontrolled, (without purpose)?
Was he not a drop of sperm emitted (in lowly form)?
Then did he become a leech-like clot; then did (Allah) make and fashion (him) in due proportion.
And of him He made two sexes, male and female.
Has not He, (the same), the power to give life to the dead? note: we and ur are plurals of respect