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Well good luck, with spelling like that you're going to need it!
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
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.
The statement is true that a sampling distribution is a probability distribution for a statistic.
No, it is the name given to the Gaussian distribution.