No, it means - you should not say that to me because you are not better than me. Example; A man is married, he goes to bed with another woman who is not his wife: his wife finds out. The man's wife, 6 months later, goes to bed with another man, her husband finds out, he shouts, "How could you do that to me!? To us!!?" - She says, "You've got a nerve!".

no it means that you are being rude or obnoxious or is doing something he knows is wrong. Its not a good thing to say to someone. But sometimes (not often) It can be used to say that some one is brave ( man, that guy has some nerve to ignore the police) ... but it is more so used as an insult.

It means your audacious, cheeky, insolent.