The DSi's memory card is only for photographs and music. It cannot run code, or run anything on the memory card, it completely lacks the ability to. It is for storage only.
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You don't. The DS Lite doesn't have an SD slot; only the DSi does (including DSi XL.)
It is a card that can hold lots of games but you can only use it on the DS (not the DSi or 3DS) hope I helped! :)
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.
You can download unlimited, full version Nintendo DS and DSi games and easily transfer them to your DS / DSi using: http://www.squidoo.com/Download-DS-Games
Yes, you can play DS lite games on the DSi as well as the DSi XL