1. I forgive you. (Formal) 2. It's fine./It's OK. 3. Don't worry about it. / No worries. They all can be used in combination.

Both are correct. It's okay is slightly more common. And they're both responses to a somewhat minor offense (i.e. Someone bumping into you). For more serious offenses, you might say "I understand" or "I forgive you."

Essentially the same. Either can be used in response to an apology if there is a difference I think - "that's ok" refers more specifically to the thing the person is apologizing about, "it's ok" refers more to the result of the thing the person is apologizing for. However, I think I would use whichever came to my mind first without thinking about it.