If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change?
The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one.
There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true.
If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect.
No, it is not.
If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]
When the sample size is small
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
There is no such thing. The standard error can be calculated for a sample of any size greater than 1.
The standard error is the standard deviation divided by the square root of the sample size.
The standard deviation would generally decrease because the large the sample size is, the more we know about the population, so we can be more exact in our measurements.
In general the mean of a truly random sample is not dependent on the size of a sample. By inference, then, so is the variance and the standard deviation.
You cannot from the information provided.