Dorsetshire, or the county of Dorset, is in the southwest of England and rubs against the coast as well as the county in which Persuasion is set, Somerset. The towns of Lyme Regis and Charmouth fall within its borders.
Mary watches the various visitors enter and exit the Grand Pump Room, a large space in which men and women would gather to drink a prescribed number of glasses of the healthy mineral waters of Bath. The unpleasant-tasting water would be pumped into a glass (hence the name Pump Room), and the drinkers would mingle and sip at will.
The Pump Room, situated in the same building as the old Roman baths, is an attraction, and it is still possible to take the waters here.
Scheherazade who, like Austen, was a teller of stories, was the framing character of Arabian Nights (or One Thousand and One Nights). She manages to keep her head, literally, by weaving tales that captivate the Sultan night after night. The Sultan, having been betrayed by love in the past, does not value women very highly, but Scheherazade wins his heart (and her life) with her tales.
For the Andrew Lang version of Arabian Nights (available through feedbooks), try here. Or, there's an online edition of Richard Burton's translation here (via Sacred Texts). For the online text The Arabian Nights in Historical Context, click here.