1. The Nunchuck is attached to the Wii Remote by a wire. It is not always attached, you can unplug when you play a game that does not need the nunchuck.
2. You would need 4 Wii Remotes and in some cases 4 Nuchucks so everybody has a controller to use.
3. Yes, for boxing you need 1 Wii Remote and 1 Nunchuck each.
4. For GC games, you will need to purchase a GC Controller if you don't already have one.
5. Any game that uses the Classic Controller can also be used by the GC Controller.
6. The only controller that uses batteries is the Wii Remote. If you use it a lot, then you can get 10+ hours. Use it sparingly for more juice.
Hope that helps.