Is it possible to limit searches only to the folder the user is currently in (or its subdirectories)?

Yes, this is a built-in feature. If you'll examine a standard Web Crossing search page you'll note radio buttons for "Search the whole site" and "Search this location". You need to include the "wholesite" input with value "in" to restrict the search to items IN this folder (and subfolders). You'll find an example search form in standard.tpl.