Yes. However you will need a game card that supports multi player. You connect wirelessly to other ds systems nearby. Sometimes you can connect with just one game card. However usually each player will need the game card.
Yes, you can. The 3DS can link with the DS to play DS games but the DS cannot play 3DS games so linking for 3D games will not work.
Yes you can. You can also connect DS lite to DS and DS Lite to DSi.
Yes you can. You can also connect DSi to DS and DS Lite to DSi.
no. theDS lite is wireless to only other DS's
It must be impossible to do this but you can connect a Nintendo DS or DS lite system to a TV
there is a problem with it
Yes it is possible.
Probably can. Try it out.
Yes. Because i have both.
Yes, they can connect over an ad-hoc connection or the internet.
Yes, if there is no security (password) or the security is WEP.