>>5 Make sure you have all the Windows Updates installed. You can find out by pressing Start and typing in 'Windows Updates'. It should search and return that app. Otherwise, you can look for it yourself in Control Panel, which is also in the Start menu.
My laptop takes a lone time to shut down because it uses an SSD for caching. Do you know if your laptop has an SSD in it? How old/new is it? Not sure if that would stop it completely from shutting own, though.