Need help with Central Limit Theorem

Regardless of the distribution of the initial population distribution, as long as we take a sample of size n>30 from the population, and form a sampling distribution with repeated sampling m times:

1) It will be normal.

2) It will share the same mean as the population mean.

3) It will have less variance (σ2/n) than the population variance by a factor of n.

Is this definition correct? So the repeated sampling of m times is not important. Rather its the sample size n that's important?