No, you can't. 3DS games are not playable for the NDS or NDSi.
No, it is only playable on the 3DS.
Mario Kart 7 is a 3DS game and cannot be played on the DS or DSi.
No, there was no second Mario Kart game for the DS. There is, however, Mario Kart 7, which was released for the 3DS, the successor to the DS.
Shadow Mario isn't playable in Mario Kart 7. Metal Mario is playable, though, and can be unlocked by winning the 150cc Special Cup.
Queen Bee is not in Mario Kart Wii at all. Queen Bee is only playable in Mario Kart 7, where she is an unlockable character in the game.
My favorite character is (Mario)Luigi. But really, it is my Mii!
Metal Mario Does Not Appeared in Mario Kart Wii, How Ever, He is a Playable on Mario Kart 7, 8, and Tour
No, Mario Kart Double Dash is for the GameCube. The handheld Mario Kart games are Mario Kart Super Circuit, Mario Kart DS, and Mario Kart 7.
No, Mario Kart 64 isn't available for DSiWare. It is, however, available for the Wii's Virtual Console.
No, it is a 3DS game and can only be played on 3DS.
You can't, because that track isn't in Mario Kart DS. It is, however, in Mario Kart 7, which was the first game to have retro Rainbow Road tracks.