1) A test statistic allows to determine the critical region for a hypothesis. Sample data support a claim if the test statistic falls within the critical region.
2) when the alternative hypothesis can greater or less than the mean of the null hypothesis, it is two tailed hypothesis. If not , it is single tailed. Two tailed has the advantage to cover a broader range oh hypothesis.
3) The probability of Type I error is the probability of rejection H0 when it really is true. Type II error occurs if H0 is accepted when in fact Ha is true. Type II error has more severe consequences.