The RAW in your quoted text has the answer.
"You can alter your appearance at will" means that you can make your nose longer, your hair shorter, change the color of your eyes, etc. So because you can also change your race, you can also change those features of the new race until you exactly match a specified target.
Also not the wording in the other sentence, "Body and facial features can resemble any human or humanoid creature." If you separate the sentence into two separate ideas, removing the conjunction "or", then you get: Body and facial features can resemble any human. Body and facial features can resemble any humanoid creature. In both cases, the wording specifically allows transforming adapting your body and facial features to resemble an individual creature, any individual creature, as long as they are humanoid. The fact that it says "human or humanoid creature" seems redundant, but by separating it out into two concepts like this, it makes the rules more clear, since turning into any human is pretty much the same as turning into any person.
Since this is at will, you could even add details as you found out about them, so when the real prince says, "I can prove I am the prince! See! Here is my secret birthmark in the shape of a penguin!" You can reply with, "And here is mine!"
The real problem with impersonations would probably be things like speech patterns and manerisms.