1. I have understood sin means rejecting God, or living apart from God. That is what Adam and Eve did in Eden, rejected God, which is why we are born apart from God.
2. I have understood righteousness means wisdom of the just, right understanding, which makes person do right actions.
The mouth of the righteous brings forth wisdom, But the perverse tongue will be cut off. The lips of the righteous know what is acceptable, But the mouth of the wicked is perverse.
Pro. 10:31-32
The thoughts of the righteous are just, But the advice of the wicked is deceitful… … A righteous man regards the life of his animal, But the tender mercies of the wicked are cruel… … A righteous person is cautious in friendship, But the way of the wicked leads them astray.
Pro. 12:5,10,26
A righteous man hates lies, But a wicked man brings shame and disgrace… … The light of the righteous shines brightly, But the lamp of the wicked is snuffed out.
Pro. 13:5,9
A righteous man walks in integrity. Blessed are his children after him.
Pro. 20:7
There are those who covet greedily all the day long; But the righteous give and don't withhold.
Pro. 21:26
The righteous care about justice for the poor. The wicked aren't concerned about knowledge.
Pro. 29:7
It is possible that righteous person makes mistakes, but the difference is:
For a righteous man falls seven times, and rises up again; But the wicked are overthrown by calamity.
Pro. 24:16
"Two men went up into the temple to pray; one was a Pharisee, and the other was a tax collector. The Pharisee stood and prayed to himself like this: 'God, I thank you, that I am not like the rest of men, extortioners, unrighteous, adulterers, or even like this tax collector. I fast twice a week. I give tithes of all that I get.' But the tax collector, standing far away, wouldn't even lift up his eyes to heaven, but beat his breast, saying, 'God, be merciful to me, a sinner!' I tell you, this man went down to his house justified rather than the other; for everyone who exalts himself will be humbled, but he who humbles himself will be exalted."
Luke 18:10-14
3. Repentance means person regrets bad actions and wants not to continue doing them.
4. We repent things that we have done wrongly and want to do better in future.
5. We can be saved from the judgment that comes because of sin. But if continue in sin, we have developed new sin and even if old remains forgiven, it is not useful, if there is new one. It is like, if you wash your car and right after that mess it with mud, the washing was not useful, even though the old dirt is not there, the new one is.