Projects simply keep the state of your err... project around, so you can switch between several --say-- books and every book project will have its own files open, settings, applied, etc. It's a sort of an additional settings file :) ST can't have enough of them! But if you look at them as (ranked) layers of settings/preferences/whatnot, it kind of stops being too overwhelming.
I don't think your problem is clear to me. Dragging folders onto ST should open them no problem and add more to the side bar; expanding/collapsing subfolders within a top folder should show/hide them, and all expanded folders should stay expanded when adding more folders. Everthing's working fine here.
If you are, however, opening ST from the command line and passing it a directory as argument, by default it will do something rather annoying: it will open a second editor window, so it will look like the other folders have all of a sudden vanished from the sidebar. Again, I believe there's a setting to change this behavior.