Maybe they have changed things, but in my experience, there was nothing to pay at NVC. They really only hold on to the approved petitions until requested by consulates, at which point they mail them overseas in batches.
Once received by the consulate, you should get packet 3, which is the instructions pertaining to the medical, police report, paying the visa fee etc.
The NVC part of the process used to take a week or two. I believe it can now take months, depending on the consulate. I would think that Warsaw K-1 interviews for 3rd party nationals would unfortunately not be prioritized.