Here, the narration refers to a “card”, which is more properly known as a calling card. A calling card -- or visiting card-- is defined as “a card bearing a person’s name and address, sent or left in lieu of a formal social or business visit; a visiting card” (OED). Originally a Parisian trend, these cards were either sent or left at a person’s place of residence to denote that acquaintance had formally visited while they were away or later intended to visit them (Robert Chambers, The Book of Days, np).

Blaize Castle -- actually spelled Blaise Castle -- is a structure located in Bristol, UK about thirty miles northeast of Bath. Despite the descriptions in the novel suggesting that it is a genuine Gothic building, Blaise Castle is actually what is referred to as a “Sham Castle”. A “Sham Castle” is, as the name would suggest, a castle built in the architecture of a previous era from when it was actually built. Furthermore, Blaise Castle is not even an actual building: it is nothing more than a facade built by the merchant Thomas Farr in 1766 (Janine Barchas, Matters of Fact in Jane Austen, 78).

The pump room -- better known as The Grand Pump Room -- was a building used for upper-class social gatherings and parties in Bath. It was especially popular during Jane Austen’s lifetime (Michael Forsyth, Bath, 68) (Mabel Van Niekerk, The Ancient Roman Cities of Bath and York, 24).

"To throw light upon, clear up, explain" (OED).

"A light vehicle drawn by one horse; a chaise; also a particular kind of light chaise" or "an enclosed chair or covered vehicle for one person, carried on poles by two men; a sedan" (OED).