"Of a thing: having an attractive form or appearance; well-proportioned; elegant, stylish." (OED)

Austen uses "handsome" to describe beauty in the male and female sense

Trade - The practice of making one's living in business, as opposed to in a profession or from unearned income. (OED)

three and twenty years = 23

This number references the 23 years they had been married.

A chaise and four is a small carriage pulled by two to four horses with two to four wheels

When Mrs .Bennet says Netherfield is "let" she means someone is renting the estate.

Lucas' knighthood was made official by the king possibly due to his already social and political title of mayor

Mayoralty - the office of mayor

Sir William Lucas was mayor of Meryton