I think that I would continue the relationship, as long as I found out from you (I'm assuming you' the one in e situation). People change, but if I were to find out from someone her than you I would think that had something to hide. It's good to put everything out in the open. Just explain to you girl that what you did was wrong (and why, explanations are always good) and tell her you don't want her to find out from else because you have changed and don't want to lose her because a stupid mistake.
Yes, once a cheater, always a cheater. Personally I do not get why you would cheat on a person you are not stuck with becuase of kids, money (debt), etc. It just seems cowardly and speaks very poorly of that person. Don´t like me anymore? Tell me to my face, biatch.
It depends entirely on their attitude, and also how long ago it was. If it happened recently and they don't seem to be very remorseful about it then, no I wouldn't continue to see them. On the other hand I spoke to a man last year on a dating site who had cheated on his wife 10 years ago and was still totally torn up inside about it. He felt like he didn't ever really deserve to be loved again. I don't think that's healthy either, but my point is that the significant amount of time had passed, he clearly thought about it a lot, and he was very religious and trying to change his life and be a different person. I would never in a million years think that man would cheat again. He admitted to having had sexual addiction and going to strip clubs and things like that, but was in recovery.
It depends on how long ago he cheated and how otherwise morally upright he seems to be. I definitely believe that people can change, but I also believe it takes a long time for people to come to terms with the wrong they had done in a situation like cheating. It certainly wouldn't help to paint them in a positive light and if they're unwilling to talk to me about it i'm out.