Central limit theorem, confusion over sample size.

#1
Good morning, Im having some issues getting my head around the sample size of the central limit theorem.

Eg Thirty random observation are taken from each of the following distributions and the sample mean is calculated. Find the probability that the sample mean exceeds 5 given that X is the number of heads obtained when an unbiased coin is tossed nine time.

(Question) Im assuming there has to be some assumption about how many times this experiment (flipping the coin 9 times and counting the number of heads) is performed as only performing it once will only give u a single value. This seems pretty pointless for the parent population.

(Question2) It states that the central limit theorem applies if the sample size is >= 30. Im assuming this refers to taking 30 values from the parent population at random and then calculating the samples mean and variance?

Thanks for your time