Sense and Sensibility (novel)/Headscratchers

Did Colonel Brandon and Willoughby actually fight or something when they met in London for the first time after Brandon learned what he'd done to Eliza?
In Chapter 31, Brandon tells Elinor of how his ward Eliza (the daughter of his doomed sweetheart Eliza) disappeared and how he discovered upon finding her that she'd been seduced and abandoned by Willoughby (along with his child). When Elinor asks if he has seen Willoughby since this discovery, he replies yes, and this follows: "Elinor, startled by his manner, looked at him anxiously, saying,"

""What? have you met him to--""

""I could meet him no other way. Eliza had confessed to me, though most reluctantly, the name of her lover; and when he returned to town, which was within a fortnight after myself, we met by appointment, he to defend, I to punish his conduct. We returned unwounded, and the meeting, therefore, never got abroad.""

"Elinor sighed over the fancied necessity of this; but to a man and a soldier she presumed not to censure it."

A footnote in my edition translates "met by appointment" as "Met to fight a duel." Is Brandon, as a soldier, being figurative, or did he really beat Willoughby up for what he did to Eliza? Three cheers for him if he did, of course, don't get me wrong, but it's just the last thing I'd expect in a Jane Austen novel.


 * That is what that means. Willoughby has effectively unmanned the Colonel by impregnating his ward and besmirched his honor. Brandon, being a man of honor, can not let Willoughby get away with this with out dueling with him on the field of honor and, ostensibly, teaching him a lesson. Even if Brandon were to die or to lose the duel his status as an honorable man, the protector of his household would be restored. Willoughby's actions betray him as a dishonorable man, for an honorable man would never have had sex with a woman he wasn't married or betrothed to to begin with. A duel in the Regency period would be done with pistols and generally they both aimed away. It was the act of the challenge and the meeting that made it valid rather than an actual contest for life. It's also interesting to note that the reason that Elinor is scared or startled by this is not just the implied violence which would worry a well bred lady. It's that dueling was illegal at the time. The Colonel would not have beat up Willoughby because that's not how gentlemen settle matters of honor.

Why exactly did Elinor fall in love with Edward in the first place?
I'm the one who added the Informed Attribute entry to the main page, because this honestly does bother me about the book. Don't get me wrong, I love the book and Austen is my favorite author. But she really doesn't give us a whole lot of explanation for what happens between them. Do they spend a lot of time alone together, talking (like Thompson and Grant in the Ang Lee film)? Somehow, without a whole lot of description, it comes to pass that Elinor's in love and everyone is aware that Edward is returning her affections. It's just sort of odd.
 * After Edward moved into Norland with the John Dashwoods for a few months after Elinor's father died, they spent a lot of time together and are already in love by the time the main events of the novel (the Dashwood women moving to Barton) begin. Maybed we need a Hooked Up Before equivalent of Hooked Up Afterwards...