One wonders how a girl who had no social skills in Chapter 3 suddenly became so socially adept -- has she been reading books on how to get along with people?

It's more that both Harry and Draco were mentally handicapped here. Draco has the glamorous dream of being the dark overlord who controls everything from the top, his orders unquestioned and his name spoken in hushed tones. Harry has the habit of trying to think up an ingenious plan by himself, and it just didn't occur to him to get other people in his army to do strategy planning. Tactics, sure, but not strategy.

Hermione, in contrast, is perfectly used to learning from others, and doesn't have particularly grandiose ambitions. And maybe Quirrell casually hinted that some of the people in her army were good at planning things. It seems the sort of thing he'd do, to make his plan less brittle.