In most contexts, they are opposites. So you could say: "I will DO nothing else", or "I will NOT DO anything else". In your question, it's not clear if you are the customer or the shop assistant. If you are the customer, you could either say: "I will pay this amount. Nothing else." or, more commonly "I will pay this amount. No more." If you are the shop assistant, then the first part of your sentence would need to change. For example: "The total cost is this amount. Anything else?" or "The total cost is this amount. Nothing else?" So, if you are using the two words on their own as a question, they are both valid. "Anything else?" = "Nothing else?"

I'm not sure I understand the question. Do you mean when you're paying for something in a shop and you're asked if you want anything else? Or are you talking about when you aren't willing to pay over a certain amount for something? In a shop, you're going to hear "anything else?" or "is that everything?" a large percentage of the time. 'Nothing else' works, but you're not going to hear it too often I would suspect.

'Pago esto nada más'. Verdad Ana? O sea, 'esta es la cantidad y no hay que pagar más de eso'? Entonces... 'Is that all I have to pay?'