What is the (or is there any) difference between 3DS and NDS games? Is it possible to play 3DS games on NDS emulator?
As the name implies, the NDS is the earlier version of the Nintendo 3DS.
The 3DS has better graphics (and sold better). Concerning the ROMs I think that will just be a tug of quality, because the 3ds is better I think the NDS will be substandard to its brother. I think that a ROM for the NDS cam work on the 3DS but I am quite sure you cannot use the 3ds ROM on the NDS because of its backward compatibility
It is not possible. Although the structure is more or less the same, the 3DS has a new firmware, which has yet to be emulated. There is no 3DS-emulator out yet, but you could hack 3DS-roms like normals ROMs, because the system is still the same.
Just to re-iterate what the other posters have said:
This all comes down to backward compatibility, as does every other device. A newer device will generally play old content (with a few exceptions). However, an older device will not play newer content; this is either due to drivers, graphics, core framework and the like...
As Looper advised - there is currently no 3DS Emulator out as of yet. So in short - No, it isn't possible to play 3DS games on a standard NDS Emulator.