Your first option, how could I not forgive you, feels the best to me. It has a sense of "of course I do", almost like it's out of the person's control - it's not even about what they want, they're sort of compelled to forgive the other person, because they're their best friend, you know?
The other two have that sense of wanting to forgive, so that feels like a different tone, like the forgiveness is a decision being made. The emphasis is more on that word, want. It's also a little more complex - just because someone wants to forgive someone else, it doesn't mean they can. Some things are too much, and can't be forgiven!
Your last two examples sound fairly formal written out like that, personally I feel like they're more natural with why wouldn't I and why shouldn't I. They both mean the same thing, but the tone for the first feels more like "is there a reason why I wouldn't?" while the second feels more argumentative, like they want to forgive you and they're challenging you to give them a reason not to.