Islam teaches that God is the one who judges, and that He will be just and forgiving (etc). For those who have not heard the message of Islam, they will be judged according to their actions - just like those who are Muslims. Their actions and the context of the actions - the environment, what they know etc are all part of what need to be considered for justice to be done.
God in the Quran actually specifies that it is NOT only Muslims who will go to heaven - Chapter 5 - AL-MAEDA 69
"Surely those who believe and those who are Jews and the Sabians and the Christians whoever believes in Allah and the last day and does good-- they shall have no fear nor shall they grieve. "
'whoever believes in God, and the last day AND does good' - specifies the general criteria God says will be used, and those who pass these (Muslims and non-Muslims) 'will have nothing to fear' - i.e. will be in heaven.
TG123: A Muslim is not guaranteed heaven - we are at the mercy of God's judgement. A non-Muslim who is 'born again' and lives a sincere life of faith etc afterwards is given glad tidings of God's mercy and forgiveness and the prospect of eternally being in the presence of God in heaven. They need faith and good works. So, I'd say 'no a person who does convert to Islam and has faith in God and does good work etc - will not find themselves in Hell eternally according to what Islam teaches'. God may admit to heaven straight away, or may require a period for some souls in hell to purify them before going to heaven... each will be judged individually.
Let me ask you hypothetically, you have a daughter aged 15, a person kidnaps her, rapes her and then muders her. Immediately after that he realizes he had commited a sin. He seeks forgiveness from God. So in your understanding he owes nothing to the parents of the deceased. Life goes on. I cannot appreciate or understand this justice. If I am passing someone in street and un intentionally rub shoulders with someone and say I am sorry then I can undertsand that person can say apology accepted and the matter is finito. But you cannot kill someones child and apologize to God and say matter finito. There has to be accountability to the family of the victim. Sometimes the only way they can come to terms with their loss is to see justice happen to the murderer.