Vocabulary in Persuasion

"Drawing-rooms" is short for "withdrawing-rooms," rooms where men and women would retire after a meal.  Usually, the women went to the drawing room while the men either stayed at table and smoked or withdrew to a room for smoking.

In the 18th and 19th centuries, vanity was usually applied to women and pride to men. In this case, Austen is consciously using the term to draw attention to Sir Walter's focus on his looks.

"Patents" are the types of documents that elevated Sir Eliot's family to Baronet status.