All 3DS games are only playable at Nintendo 3DS and 2DS. Due to the difference in sizes of the cartridge of 3DS games, It is impossible to fit in 3DS games in Nintendo DS or DSi consoles. You can easily compare the difference of 3DS and DS games in their sizes, Also it was marked in colors too. (DS games are black cartridges while 3DS games are mostly white cartridges)
No, it will only work for the Nintendo 3DS or 3DS XL.
Unfortunately no, the 3ds game cartridges do not fit in regular ds slots.