"to cut off some unnecessary charities..."See in text(Chapter 1)
This is biting satire—the first expense to be curtailed is giving to charity. In the 19th century, private charity was a primary source of help to the poor because institutional charity was not widely available. Giving to local charities was expected of those in Baronet Eliot's class.
"he had purchased independence by uniting himself to a rich woman of inferior birth..."See in text(Chapter 1)
Austen records a very common situation here: a man with a title but no money marries a woman with money but no title. The man marries for money, the woman for a title.
"as she travelled up to London with her father, for a few weeks' annual enjoyment of the great world...."See in text(Chapter 1)
In rural areas of England, the country gentry, like the Eliots, would go to London for several weeks to see and be seen. Going to London was often the high point of the year for wealthy people like the Eliots.
"and one remained a widower, the other a widow..."See in text(Chapter 1)
It is unusual that neither should marry. Men with property and a title were expected to marry if a suitable partner was available, and widows were vulnerable socially and economically.
"Vanity was the beginning and the end of Sir Walter Elliot's character..."See in text(Chapter 1)
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.
"in the first year of Charles II..."See in text(Chapter 1)
Charles II ascended to the throne in 1660. His father, Charles I, was executed by an act of Parliament in 1649, and what is known as the Commonwealth Interregnum (rule by Parliament) lasted until 1660.