How does Justice work in Catholicism?

So my BF is a Muslim, a Shia Muslim to be precise. I am a nominal Catholic; none of us are all that religious. But he has been getting more practicing this Ramadhan.

We are talking about things and he said that even though he has issues with the high demand nature of Islam, and very much with what he calls "Muslim culture" (i.e. things which are found amongst Muslim communities but not necessarily theologically within Islam like no-dating / arranged marriages, gender segregation, authoratitve infantalizing culture, etc); he says that he likes the sense of justice within Shia Islam. Here is how he describes it:

• Quran 99:7-8 - "So whoever does an atom’s weight of good will see it. And whoever does an atom’s weight of evil will see it."
  • So all good and bad deeds will be accounted for on Judgement day
• God is fundamentally just, so everything will be accounted for
• Sins against others can only be forgiven by God if the victim forgives you first.
  • So you cannot be serial killer and then get God to forgive you go to heaven if the victim has not forgiven you first; Justice would be served and the perpatrator will be punished
• Sins against God on the other hand; well God is forgiving and merciful
• If you are a believer, God will show his mercy and can very will forgive you for sins done against him. He may also show mercy against sins done to others provided that the victim forgives you first
• If you are not a believer, well you have no obligation towards God - you cannot be held liable for say not fasting if you are not in the faith (but also you are not getting the rewards that believers get for their devotion cause you are not doing it)
• Non-believers like believers still get rewarded for good deeds done towards people all the same
• God can forgive all sins in this world (caveat on the forgiveness of the victim); but in the afterlife he won't forgive idolatry / polytheism. At the same time, no can be held liable for not believing in Islam "if they did not know the truth of the matter"
  • So in effect yes non-believers can very much get into heaven though this as per my BF is debated based on how conservative or liberal the cleric is. Though the liberal position does seem more logically in line

I found this fascinating and he asked for more info on our position but I realized that well my family being nominal I do not know much. I know that we reject the evangelical position that "Works don't matter; it is all about whether you believe that Jesus is the Lord. If you do you are saved no matter what. If you don't you are saved no matter what". But at the same time I really do not know much. Care to help me out!