You can use any Wii games or Wii U games and software. Wii U games don't work on Wii, however, and the Wii games require the TV screen.
Yes, however you'll still need the wiimote and nunchuck for those games.
The Wii U is a different console to the Wii. The Wii U however is compatible with Wii games and accessories.
No, the Nintendo Wii cannot play Wii U games
No. Gamecube game were compatible with the Wii but they're no longer compatible with the Wii U. Wii games are however still compatible with the Wii U.
The Wii U can play all Wii games since it is backwards compatible.
No, the Wii cannot play Wii U games. It's actually the opposite - the Wii U can play Wii games.
Yes the Wii U is backwards compatible
No, the Wii U cannot play Nintendo DS games
Yes, the Wii U is backwards compatible with Wii games. You need to insert a Wii disk, then go into Wii Mode by selecting the option from the Wii U menu. You'll need a Wii controller to use Wii Mode.
Yes, the Wii U is backwards compatible with Wii titles. (It cannot, however, read/play Gamecube games.)
The Wii U is compatible with Wii games. There is no difference in the disk sizes. (Be aware that the Wii U does not support Gamecube games.)
As long as the game is from the same region as the Wii system, it will be compatible.
Yes as the Wii U is backwards compatible with all Wii Games, Downloads and Peripherals, but not GameCube ones