I'll take your last question first:
do you think a couple can be really happy together even though their sex life is non-excisting?
Yes, I think a couple can have a happy married life even without sex. Not me personally...I couldn't do it. But I do know of some who have done so. I'd say that this type couple is definitely in the minority, but yes it can be done. It would have to be a mutual understanding. If a sex filled marriage became a sexless one depriving one or the other of something they desire or need, then you've got some major problems.
What if your sex-life is dead and your partner never finds out abt it, is it still unforgivable?
My personal opinion: Unless both partners have agreed to an "open" marriage, then any sex outside the marriage wrong. You got married for better or worse...and the no sex part would be part of the worst. If a once sex filled marriage has deterioted to the point where one or both can't stand the touch of the other, then serious counseling is needed or a divorce.
If one strays and has an affair and keeps it a secret, the question of if its forgivable is moot. The other doesn't know. Can the guilty party live with it is the real question.
If one has an affair and its found out it could be forgivable depending on the circumstances or it could be the straw that ends the loveless marriage. I've seen that happen as well.
Can you live on together? Can the cheater live on as usual?
Each person and each situation is different. It's up to each person and couple to decide if they can live together or not. Whether they can live on together or not, some serious counseling is needed.
I've known some cheaters who don't think twice about what they've done. Pretty f'd up, I'd say. I've also been the leaning shoulder for friends who were absolutely miserable after they strayed...it can be one of the most miserable situations to be in if you're someone who believes in the sanctity of marriage.