1. You can shutdown your PC from within the Bigbox UI, which is part of the premium license.
2. Yes.
3. That will be down to whatever emulators you choose to use as to how they handle controllers, multiples of the same controllers can be a little problematic as they may not be seen as individual controllers.
4. Launchbox itself is portable, as are most emulators, so as long as you choose the right emulators, yes.
5. If you buy a license for Bigbox and you setup your emulators correctly then yes you will just transition from the Bigbox UI straight into a fullscreen game.