There are only a tiny handful of 'DSi games', games which specifically need the DSi's camera to play. Most are even DSiware. So technically all DS game cards will work just fine on a DSi, there's no need to do anything to get them working.
If you want the same game progress, yeah. But you can just go to the wii channel on the wii u and you could play your wii games fine.
You need a PS2 to play the games not a PC
You Dont need a controller. I have p64 too and I`m playing Turok 3 just fine
You need a console to play console games. Computers play computer games and a PS3 will play PS3 games or the Same for the Xbox 360 and the Nintendo Wii.
No I don't think so I have terminator 3 Rise of the Machines for ps2 and the remote worked fine.
A proxy is not required to play games
You do not need to have a Memory Stick inserted to play games if you have UMDs.
Yes, regular DS games will play fine.
An emulator
No but if you want to play original xbox games on the 360 you need one, but a flashdrive would suffice.
Normally you don't need to buy any games to play it's sequal.