Should I take separate soil samples for each of my fields?

Take separate samples. Each field has its own history of crops, manure and management, so each will have a different nutrient picture, and mixing them gives you an average that fits none of them. The rule is, one composite sample per field or per uniform area. Even within one field, if part of it looks clearly different, for example a low water-logged patch, a sandy strip or an area that always grows poorly, sample that part separately so you can manage it on its own. So for your three plots, prepare three separate composite samples, each made by mixing 8 to 10 sub-samples taken in a W pattern across that plot, and label each clearly with the field name, survey number and the crop you plan to grow there. That way each field gets its own card and its own correct recommendation. Keeping them separate is the whole reason the recommendations are useful.