In .desktop files, there'll be a line for the icon, something like "Icon=firefox" or "Icon=chromium-browser." When you see this, is there an easy way to determine the actual path to the icon that's being indicated? How does KDE translate that into an actual path?

KDE follows the XDG Icon naming specification here. This involves first looking in the current theme, then in it's fallback and so forth until you have run out of places to look. The name of the icon may also be shortened at each step to try and find a matching name (by breaking it down on dashes)