Sin, faith, forgiveness, and repentance

[Bootstrap]

This is a Bible study thread, open to people who believe in simple obedience to Scripture. I would like to request that people in this thread follow these rules:

1. We will focus on passages that directly address the relationship between sin, faith, forgiveness, and repentance. We will use other threads for other passages.
2. We will start by asking and answering simple answers about what these passages say - objective things that we expect we can probably agree on. If we can discuss more than one passage without losing focus, that's fine, if things get too chaotic, I may request that we focus on one or two passages at a time, we'll see.
3. We will talk about the text, not about other people.
4. We will focus on how we apply the text ourselves, not on how other people should. But we will start by understanding what the text meant when Paul wrote it before we go on to application.

This particular thread was inspired by this question from Sudsy and Soloist's response:

And if we do sin, even by sexual immorality, sin has it's consequences but God is faithful to forgive us of all sin and give us restored fellowship just as if we never sinned. Right?

If we repent and stop doing it. God will forgive us. God does not forgive unrepentant sin.

What scriptures are best to explore these questions? Is faith and trusting God also a factor? Are there a small number of scriptures that are particularly helpful to start with? Are there scriptures that are particularly confusing that might make sense to talk through and better understand?