Central Limit Theorem guides, where, question

water2012

According to Central Limit Theorem, if a sample size of n (where n >= 30) is taken repeatedly from a Population, then mean is calculated from each such sample and then those means are plotted in a graph with probability on Y axis and mean on X axis then it takes a form of Normal Distribution.

My question is how many times these samples need to be taken, is there any formula which guides this decision?

Also, if we calculate the Mean and Variance of Normal Distribution of sample means thus formed, the Mean of the distribution will be equal to the underlying Population mean and Variance of the distribution would be Population SD upon square root of sample size, right? Pls confirm, i am a bit lost.