Question: What is the difference caused by using “nope” instead of ”no”?

Is it used because “nope” sounds better and not straight like “no”? In some situations, it feels like *nope* is better to use than *no* even though it adds 2 more characters. What is the reason why many use it?

Answer: 
"Nope" is informal. You wouldn't usually want to use it, for example, answering questions for a job interview, but it would be an appropriate answer to a friend's question "Have you seen that movie yet?"
I think the context has a lot to do with how the word Nope is perceived:

1. Somebody asks you for something.

> 
> - Will you do something for me?  
> - Nope. << Rude
> 
> 
>
2. Somebody asks for information.

> 
> - Is your name Sam?  
> - Nope. << Playful / informal
> 
> 
>

Maybe the word Nope implies a casual, relaxed attitude, which in some cases may come off as dismissive.