Note 1: (direct proposal of marriage)
To the modern reader, this might seem like a strange way to propose-a letter, to us, seems impersonal, but it was fully in keeping with the practice during Austen's day. It was even expected that a proposal would come by a letter, and not in person.
Perhaps it was seen as giving more freedom to the lady to refuse, because it is much more difficult to say no in the man's presence, than it is to write the same in return to his letter.
In addition, an engagement was rather binding on the gentleman. He could even be sued for something akin to breach of promise, if he broke it off. Thus having evidence of a proposal and an understanding would be of legal benefit to the lady, as the man could not deny having made his offer.
In Pride and Prejudice, when Darcy writes his letter to Elizabeth after the Hunsford disaster, the first thing he does is assure her that he is not repeating his proposal to her.
Be not alarmed, Madam, on receiving this letter, by the apprehension of its containing any repetition of those sentiments, or renewal of those offers, which were last night so disgusting to you.
In addition, it was not proper for a gentleman and a lady to exchange letters unless they had an understanding. After leaving Derbyshire and returning to Longbourn to commiserate with the family over Lydia's disgrace, Mrs. Gardiner is expecting to see Elizabeth receive a letter from Darcy; she was expecting Elizabeth to receive a proposal.
The best example in Jane Austen's novels of the practice of proposing by letter comes in Persuasion, where Frederick Wentworth writes his beautiful letter of love. Persuasion, Volume II, Chapter 11.