One thing I am confused about on this game: do the players take turn while they actually play out the scenes? I know the turn order is used to voice thoughts about the scenes, but when the scene starts are the turns maintained or is it just freeform roleplay? Thanks.
Yes, there's no turn sequence once you've established characters and thoughts.
There are two things preventing the roleplaying from being chaos, though.
In my experience, there is a mix of uncertainty and directness among players during a scene. Sometimes everyone will be tentative, and that's ok; those scenes are good practice for everyone. Sometimes one player will start off driving the action, but that just pulls the others into it. Sometimes everyone will be jumping in and talking, and those are golden moments of engagement and roleplay. In any case, scenes are short and an "unbalance" in who ends up having made the contributions isn't a problem. There is always next time for the game and the other players to do something different.
The last two steps of the scene setup, choosing characters and revealing thoughts are done in reverse (CCW) starting with the player to the right of the one making the scene as written in p.29
However, there's no mention of a turn order once the scene begins. Players take up telling the story in response to each others' depictions of whatever's happening. You can see that happening in the play example at p.39