Nope. It's not possible, except with a gameboy advance though.
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It must be impossible to do this but you can connect a Nintendo DS or DS lite system to a TV
Yes you can. You can also connect DS lite to DS and DS Lite to DSi.
no. theDS lite is wireless to only other DS's
Yes, if there is no security (password) or the security is WEP.
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.