Will all random samples from a given population have the same mean? Provide an explanation with your answer

Short answer No.
ExplanationSuppose you have a sample of coins that have the date of production on them. They go from 1990 to 2000 inclusive. There are 100 coins in each year. That means there are 1100 coins because there are 11 years. Now you pick out 10 coins without replacement. Let's say all of them are from 1999. Then the mean is 1999.
If you start again and pick out 10 and get 3 years 4 from 2000 2 from 19954 from 1992
Whatever the mean is, it is not 1999. The mean of the second batch is 1995.8!