Unless you have an external drive specialized to do so, no.
No.
Yes, the Wii U is backwards compatible with Wii titles. (It cannot, however, read/play Gamecube games.)
Mod you Wii
No. This is not possible on the Wii or the DSi.
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.
no, the wii can't play games on the internet, just like the PS3.
No. They run different operating systems.
yes all of them if possible to fit
If you download the Nintendo Channel (free), you have the option to be sent messages when new games come out for Wii or WiiWare
No. But, if you soft mod your Wii, you can play old platform games through an emulator.
No, wiiU games are only made to be used on the WiiU, though the WiiU has been made to be compatible to Wii games.
Yes, but only gamecube and wii games will work in the wii console. You plug the gamecube controler extension into one of the four holes in the compartment on the top of the wii, and insert the gamecube disc.