No, there is no (official) way to connect the DS to a laptop.
With special homebrew hardware, you can connect directly to your DS but this isn't used much. Usually, there are memory cards which can plug into a special adapter (called a flash cart) which you can use to access files on your DS.
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For the most part, yes you can. If you want to connect with pictochat or DS games (including DS Download), you can connect between a Nintendo DS and DSi. However, for DSi specific games, such as DSi games and certain applications, the Nintendo DS will not be able to connect. But, note that certain DSiWare games that can DS download play still can be connected to the Nintendo DS.
no
It must be impossible to do this but you can connect a Nintendo DS or DS lite system to a TV
On the main menu screen, select "Roadie Play", choose whatever way you want to play, and follow the on-screen instructions. Then on your Nintendo DS, choose DS Download Play and wait for the DS and Wii to connect.
Use WI-FI, first U have to connect UR DS to the Internet.