It is an assumption to hypothesis testing. I can not comment on the significance of a violation of these assumptions without knowing how the non-random sample was taken.
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There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.
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It can be but it is not simple random sampling.
Simple!
Random Sampling