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You must sample at 2 x the rate of the analog signal (2 x the analog signal frequency).
The central limit theorem basically states that as the sample size gets large enough, the sampling distribution becomes more normal regardless of the population distribution.
Yes, and more so for larger samples. (It follows from the Central Limit Theorem.)
It takes too much time and effort to check each transaction.
If the signal is bandwidth to the fm Hz means signal which has no frequency higher than fm can be recovered completely from set of sample taken at the rate