This is used in statistic to know whether to accept or reject a null hypothesis or alternative hypothesis
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The answer depends on what the test statistic is: a t-statistic, z-score, chi square of something else.
Normally you would find the critical value when given the p value and the test statistic.
Given any sample size there are many samples of that size that can be drawn from the population. In the population is N and the sample size in n, then there are NCn, but remember that the population can be infinite. A test statistic is a value that is calculated from only the observations in a sample (no unknown parameters are estimated). The value of the test statistic will change from sample to sample. The sampling distribution of a test statistic is the probability distribution function for all the values that the test statistic can take across all possible samples.
No The test statistic F-Test is a sum of squares, which by definition of squaring a number it must be positive.
You can calculate a result that is somehow related to the mean, based on the data available. Provided that you can work out its distribution under the null hypothesis against appropriate alternatives, you have a test statistic.