You have unintentionally asked a highly contentious question! XD There is controversy over whether the book Hwarangsegi, which is the only existing record of Misil, is a genuine historical record or a later forgery. So, depending on whom you ask, she is either a historical feature or a fictional creation. At any rate, even if the book is a forgery it predates the show (and the novel it's based on), so she wasn't created specifically for the show, no. But this imagining of her as a ruthless politician and would-be queen is a fictional creation that does not directly reflect her entries in the Hwarangsegi, so Misil as we know her from the show is definitely fictional.

Oh, his family name is Lee, and that hat, called 갓(gat) was standard attire for married noblemen of the time period. It's woven of horsehair!