I think it's geometry?

[DebW]

This is very exciting! It seems to mean that while I already feel limited on my current bike after just a few months, a well-fitted road bike would give me much more "grow room," yes?

yes.

I think I've heard the term "compact frame" but I'm not sure I understand this -- There seem to be "generic" frames (man-bikes, as we've been calling them), WSD frames, and are these "compact" frames something else? Are they specifically related to the sloping top tube? Do I understand that this "compact" thing, sloping top tube thing, and the WSD thing mostly affect how my upper body reaches the handlebars?

Compact frame just means that the top tube isn't level. Frames designed for either men or women may be built with either horizontal or sloped top tubes, but for small women it's easier to design a frame with a sloping tube. Traditional frames all had horizontal top tubes, so this is kind a new thing, or maybe a marketing gimmick. Having a sloping top tube may or may not affect how your upper body reaches the handlebars.

Now -- that handlebars/saddle thing -- is this the flat top part of the bar, the drops, or the hoods?

The top of the bars.