The male lead is called Sir Charles, V. If this title is associated with knighthood, it is not inherited. However, the title of baronet, also styled "Sir," can be inherited. So if his ancestor were a baronet, it would be appropriate to address Charles as Sir. Otherwise, it would not. If this is clarified in the film, I missed it, which would be my own shortcoming.
In order for Chelsea in the 21st century to see Sir Charles in 1799 through the mirror on the same date in their respective years, the phase of the moon needs to be in sync for the same date across two centuries of time.