Yes, of course, I can see that if you have an extremely small sample, then the _resolution_ of your results will suffer. However, I think it's much more important to ensure unbiased sampling than it is to ensure a large sample size.
For example, if you sample 1% of the population in a fair and unbiased way, that would tell you something with a much higher degree of confidence than if you sampled even 10% of the population in a biased way (or in a way such that you don't know whether you are biased or not).
Yes, it's necessarily true. If your sample is small you are necessarily subject to large sampling error.
In essence: the individuals you happened to pick (even fairly) are overrepresented, and the rest are underrepresented.