I don't think I can play your game, sadly, but almost entirely because I can't remember all the characters in all the books! One of the reasons I have an enduring love affair with them is that I can re-read them at an interval of about 3 years and it's almost like I've forgotten them.
Can't for the life of me think who Sarah Fane is, for e.g.
But the ones I can remember:
Heroes: Kit from False Colours, Hugo Darracott (thank you for the reminder), Freddie from Cotillion (he's such a gentleman!) and probably several others whose name I can't think of but including nearly all of the men in Masqueraders; oh and Lord Anthony Fanshawe, aka Jack someone or other (goodness - is he in the Black Moth?).
Heroines: Léonie, Sophy Stanton-Lacy, Mary Challoner, Arabella, Frederica and Penelope thingy (another one who dressed as a boy! - can't think what the heck her book was called though...)
I am most like: probably the managing termagant in the Grand Sophy! The bluestocking that her cousin Charles was engaged to, begins with E... - she is also in my Most Irritating Female list, along with Julia from Civil Contract.
Bits that make me laugh - lots! Much of the Grand Sophy, Cotillion, Friday's Child, Arabella, Frederica; Rupert and Léonie's antics; Horry Winfield (is that her name?) - Marries Rule, who may or may not be an Earl.
Most engaging moment with a child - well, I quite like most of Frederica's little brother's antics; and I love the bit in Sylvester where his small nevvy escapes from Button and is seen legging it away somewhere, his little legs twinkling. He's a very engaging child, actually. Him and his Bad Man.:)
Proposal - goodness, they don't really stick with me. I think it might be Arabella's though - because she can't accept.
Most touching moment: The section in These Old Shades where the Duke of Avon denounces M.Saintvire, and his chase after Léonie. Has me in bits every time.