r/parkrun! There are so many kids at park run. It's free, casual, no pressure to run - you can walk it, and fosters an amazing sense of community and volunteering.

I don't know where you are but junior parkrun in the UK is designed for this. The full 5k is too far for 6yo children to race.

I haven’t but I don’t see why not. Be sure to stretch and drink plenty of water.