Can a lawyer demand that interest and court cost are part of what is legally owed prior to a judgment?

Question Details:

I am being sued. I have not admitted I owe the debt. I just offered to settle it. They have jacked up the amount to what they "pray for" in the lawsuit. The creditor has told me that they are interested only in the original debt amount. Court costs are incurred if it goes to court right? And the papers were not served by a special server, they were served by the sheriff. And the filing fee. This should not be part of the settlement negotiation either should it?

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