You choose to forgive. Believing in it will make you more open minded, and you can understand a person better while doing it. Of course, forgiveness has boundaries, but that doesn't mean we should grudge people for it. I believe in forgiveness because it is a way of grace, trust, and learning.
Whether or not someone deserves to be forgiven depends on the infraction. The more serious the transgression, the less likely I am to forgive. Some things are beyond redemption, if somebody betrayed me for instance, I would never forgive him/her. In fact, I would kill them. Sounds a little extreme, but why should I show them mercy?
Nothing is ever completely forgiven unless it is completely forgotten. Hypothetically, you have two friends (A and B) that you feel the same about. One friend (A) wrongs you in some way but you patch it up. Sure, you may become good friends again but you would always find friend A less of a friend than B. You would always trust them a little less because of what they did. Sure, the other friend may do something as well but that would just mean that you mistrust them both a little. You could also do something against your friend to balance the scale but that just means you both mistrust each other a little. As long as you remember what happened, you will always hold some level of mistrust.