Fluoride is toxic and should be avoided to begin with. The idea that you would not rinse to keep the toxicity in your mouth longer is beyond stupid.

Best core exercises? Squats and Deadlifts. Start light and master the form. Then gradually go heavy. I no longer do ANY ab-specific exercises (situps, crunches, planks, etc.), and my core is like a rock. This takes time, though. Years, not weeks.