NInetendo is a very popular game console company. You can find games for Nintendo DSi just about anywhere including Walmart, game centers, Radio shack, and even at your local pawn shop.
Nintendo DSi.
Yes, you can use ds games on the dsi. My friend's sister got one for her birthday and she said you can use them in the dsi. But the Dsi's do not fit in a Ds case.
Only if you have a new one repaired from Nintendo.
Yes it has the exact same games as the old one.
Yes, the Nintendo DSi can play Nintendo DS games. The NDS and NDSi are compatible with each other and can link for multiplayer as well. There are really no such thing as 'DSi games' except for DSi-ware and one or two games that require the DSi camera, none of which are compatible with a DS. However, since the DSi has no GBA slot, Game Boy Advance games and DS games that require this slot (e.g. Guitar Hero: On Tour) cannot be played on a DSi. Flash carts and unofficial hardware won't work either, but there may be a newer version available, designed for the DSi. Another problem you might find is that if you have any Wi-fi capable games, they will only work with a WEP security enabled network (or of course a network without security), not WPA.
Buy a new one!
If you mean the DSi then no Sources: I own one
Regular Nintendo DS games are not region locked, a UK one will work on a US DSi.
Well, that is one simple question, you see it depends on the games you buy and the games you buy from the Nintendo DSI Shop too. There are some Nintendo DSI XL Systems that have pre-installed features too. It might include 1 or 2 games.
No, only GBA ones. You cannot play regular Gameboy or Gameboy Color games on a DS.
There is no difference between games on the DS and the DSI. There is one game I know that only works with the DSI. It requires you to take a picture and tap the screen to kill monsters. Check nintedo.com for mor features of the DSI.
There are a few 3D games for the DSi. Legend of Kay is one, though I wouldn't actually recommend it.