Questions

p. 43 - How does the Prince know Cinderella is a scullery maid? (October 13)
 
This is a consistency error in the original script. Here is my suggestion:
 
On page 42, Cinderella says, "Thank you, sir, but I am not a princess."
Have her immediately add: "I am just a scullery maid."
(The Prince laughs at this, thinking they are both playing his game.)


How does one become a duke/page? What is their relation to the Prince/royal family? (October 12)

Usually, a DUKE is born into this position/title and has a big estate (dukedom) that goes with it. As fares nobility, being a duke is a high as you can go without being part of the royal family; even then, some royal princes are also dukes. (The pecking order is DMEVB: Duke, then Marquis, then Earl, then Viscount, then Baron.)

A page, on the other hand, is little better than a messenger. In a feudal system, a page would be the entry point that would lead to squire, still a servant.

Chances are that a duke would be related to the royal family, while a page would be a commoner.

In a fairytale, these questions might not matter. What probably does matter is that our Duke is important (or thinks he is) but is nowhere as important as the Prince, who is royalty. It also could be that the Duke is part of the Prince's extended family, perhaps an uncle or cousin. The Page is a servant but, unlike Cinderella, he serves someone really important and, therefore, has impressive clothes (and probably attitude to go along). An adult page, as in this production, is probably more akin to a valet.

You didn't ask, but...

A scullery maid is the lowest of the low when it comes to servants. She probably would have to light (and maintain) the fire for cooking and, thus, would be associated (and covered) with cinders (ashes) from the fire.