Here's another boast that caught my eye:
The bombs allegedly cannot be detected because "they are enveloped in thick layers of lead". They could be detonated "by various methods - cellphone call, radio frequency, seismic shock or by their regressive clock".
I do believe this is a direct contradiction -- a thick covering of lead is going to stop radio waves much better than it will stop the radiation.
Yup.
Noy if most of the electronics and antennas are outside the lead. Only the nuclear material and whatever form of detonater they use, i.e, gun or lens, along with a minimum amount of other stuff need be shielded.