Yes, you definitely want to fire the pots--otherwise they're just dried mud and very fragile and will dissolve when wet.
I don't see why younger children couldn't burnish with rocks. Just have them make a ½" thick pinch pot that is small and scrape the sides really well so they are strong. If you don't have really smooth sides it's hard to burnish--you will have little dips. You can keep them leather hard in tight plastic bags
but... do they even need firing then after burnishing? I would think so -
but some of your responses were unclear on that - -thank you for your
suggestions - Leah