Do you bake the galette directly on the oven rack (on the parchment)? or on a baking sheet? pizza stone?

I'd recommend baking it on a baking sheet or pizza stone. The dough will be quite mailable before baking and you'll need something sturdy to put it into the oven.

Check out steps 4 and 5 -- you roll the dough out on floured parchment on a baking sheet, chill it for 15-20 minutes, then fill and bake it. It doesn't doesn't sound like a pizza stone enters the equation. Good luck!