You have to forgive him/her for your sake and move on. If you lack forgiveness, you will grow very bitter and this will reflect and cause problems for future relationships, and even your marriage to eventually fail. It will stagnate it, and make you grow physically ill and cause tremendous and unnecessary stress. I would avoid dating someone who still lacks un-forgiveness in a past relationship. They will eventually target and take the stress out on you, if you do something that reminds them of the offense. So unless you can handle a person like that, it's advisable in my opinion to avoid them at all cost until they forgive. They are still bitter and miserable about the cheating. Let go, before you end up hurting an innocent person because your still angry. Or seek professional counseling.
No, they don't deserve my forgiveness and that would be the end of the relationship. I pick myself up, move on with class and continue my life. Calm and quick. No anger, no screaming, no violence. The next day will be my new and first day of me being single again like nothing happened. That ex of mine wouldn't have my trust any longer.
It depends on the situation and the extent of the cheating. I might be able to forgive a singe drunken mistake- maybe- depending on the circumstances. I could never, ever forgive a long term, premeditated affair.
No. Upon entering any relationship, I make sure that it is clear to him that I won't tolerate it. I won't go digging for evidence, but if I do find out that he is, I will confront him and exit the relationship. I also make sure that he understands that he can expect the same from me. If I'm tempted to cheat, it's evidence that I'm not invested in the relationship, and I will end it before beginning another one.
Forgive them as in taking them back and still staying with them, NOPE. They already had their chance of being in a relationship with me and by cheating, he decided that he didn't need me anymore in his life.