No there isn't one. Even if there was on it would not be stable at all and will most likely have heaps of bugs.
Ipod touch is far too powerful for the dsi (the ds is 64bit-the ipod touch is closer to 120bit). There is theme's to place over the current them but that is as close as you get.
Correct, thought the tilt is debatable seeing a few clips of homebrew actually making use of...what seems to be a built in one.
there is a ds emulator for the ipod touch, but ipod touch emulator for ds, its simply not possible, the DS isnt powerful enough