I think the FP is more of a paint burnisher as opposed to a fine swirl mark remover. I use it as a last polishing step before applying protectant/finish. You might consider using #82 or #9 to get rid of your swirls, keeping in mind they may contain some fillers that will hide some swirls. Use the FP to get rid of the fillers and burnish the paint to a high shine.
You probably do not have to wash after using FP ( no fillers or silicone/oils). Nevertheless, I always wash (Z7, 1Z Perls) after polishing to check for any filler activity even when products deny that their products do this. Also any dust residual will be removed at this time. I recommend a Z7 wash and Z6 wipe down ( inspection step) prior to polish application. Dawn not necessary.
BTW what abrasive did you use with the yellow? Prep is 90% of the finished product, DO the FP with the white pad with your PC set to 6 - might as well get the Z as close to perfection as you can before the Zaino
Menzerna FP has extremely extremely low abrasive levels. Like Gonzo said, it is a paint burnisher, not a cleaner in Meguiars terms. Take it like a glaze without fillers. I would say you at least need IP to get out any paint defects.