You can import most DSiStore games onto a 3DS from the 3DS' memory management menu. You can also play Monster Finder, which is the only true 'DSi game'.
No, the DS and DSi games will not be in 3D.
Yes there is a different slot for them.
No
No, dsi games work in a 3ds, wont appear 3d though, but the dsi does not have the ability to play 3ds games.
You can play 3DS, DSi or DS games. (Note: DS and DSi games do not display 3D visuals.
There are a few 3D games for the DSi. Legend of Kay is one, though I wouldn't actually recommend it.
If they were specially designed for the 3DS, no. There is a small tab jutting out of the side of 3DS games making them unplayable on a DSi. Even if you could fit the cards into a DSi, they would not work because they use 3D technology the DSi cannot utilize. DSi games will be playable on the 3DS though.
Yes
There's no such thing as a DSi 3D. You might be mistaking it for the DSi, DSi XL or 3DS.
No. The Nintendo DSi and the Nintendo 3DS store games on the SD card, not a sim card.
The 3DS can play the DSI and regular ds games and Yes Of course the 3DS can Play the 3d games but other nintendos can not play the 3D games.
A faster processor and more RAM was added to the DSi. This will allow for better looking and smoother gameplay.