Well the first one doesn't have a nut, and the strings would float really high off the fingerboard. The second instrument does not have a fingerboard. So it would be limited to eight notes only. The last one however, looks fine. I would in fact be very curious to attempt to play it.
This isn't entirely correct, though. Well at least with the second part. Just because an instrument does not have a finger board, does not mean that you cannot change the pitch. Instead of pressing your fingers to the finger board and holding the string down, to stop the vibrations, it'd be a pinch between two fingers. Harmonics are also possible, which are possible on just about every string instrument.
As to the first one and it's lack of a nut, this instrument in it's current design would be unusable with or with out a nut. Why? Because think about where the strings would be connected to the pegs from that picture. The peg box is a solid piece of wood with the pegs stuck in it, with no where for the strings to go but out. If you notice in the picture (if you can't see I've blown it up) there's no actual strings on the instrument:
Although it's hard to see (as it's a 2D image) but the strings would barely be on the finger board rendering it fairly useless.