1. I believe so.
2. Don't think so.
3. The GamePad? I think it runs on batteries too. But you can probably just buy a charger, I've seen some around.
4. Don't know.
5. No experience buying things online.
Sorry for not being able to answer all of your questions completely, but I tried.
I don't have a Wii U myself (anymore) so I don't really know much about it. Not so sure.