There is no literal stage—the term "stage" in this case is more metaphorical with the entire dreamscape like the "stage" and Shakespeare is the one how is mostly in control of it. So there's no audience unless they consider Shakespeare an audience. There is also no hard script, just guidelines so it's more like improvisations for the "scene" prompts (ie, all of R&J and the ones listed under the extra scenes). More generic example, it's as if they got a slip of paper that said "Do something romantic" and now they have to play it out however they want to.

Characters are fully aware that they have to do these kind of scene objectives and they can play it loosely. For example if we take the Tybalt v. Mercutio duel, the two characters can be friendly with each other at first and just kind of banter and mess around, and then they can also be serious in their role and spit out lines like, "It's time for you to die for your uncouth words, Tybalt! I won't let you slander my cousin any longer!" "Hah, you're all bark and no bite, Mercutio!" or something.

This is more pertinent for the ones who "play out" a role (Romeo, Juliet, Paris, Benvolio, Mercutio, Tybalt). Everyone else can pretty much just do whatever without worrying about what Shakespeare thinks.