Can't say i've every seen any of my neons or xrays sleeping anywhere near the bottem, they usually just doze off where they'd usually be swimming during the day.
As far the the amano shrimps catching them, as someone's said the claws on an amano are really quite small. I've got some Amanos in one of my tanks, about 10 of them, ranging from an inch long, to the fully grown ones that are over 2 inches in size. Even the fully grown shrimp still have small claws, literally a few milimeters in size. They also have never been seen as being aggressive to any other members of the tank, often taking abuse and a few knocks from the other fish! Also, I'd not heard of them being nocturnal, mine are very active during the day, and seem to be less so at night. The only time I've ever seen the shrimp eating fish, is when the fish themsleves have died, and the shrimp have seen them in the tank before I've had a chance to remove them. Never have I seen the shrimp being aggressive to alive fish.
Could it be possible that you've either not got amano shrimp, but some of the more hostile shrimp varients, with larger claws or possibly as mentioned before could it be tetra disease? I don't think it would be any dodgy water perameters as shrimp are very sensitve with water perameters, and I think they'd be dying off before the fish in the tank.