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, but it's the resolution that would suffer, not necessarily the result. For example, if 65% of the population would vote for candidate 1, an unbiased sample of size 10 would indicate that either 60% or 70% of the population would vote for candidate 1. A sample that is biased could literally tell you anything, regardless of how large it is (in absolute numbers).
Not every time, surely? A sample is randomly taken, so there will be variation. Even if it's unbiased, your samples will swing between all possible extremes. So you need to take a very large number of small samples.
You can't take an "unbiased" sample in the sense that you mean here.
There's only one way you can take a completely unbiased sample: if you know exactly how everyone will vote in advance and select them carefully on that basis. But if you already know how everyone will vote in advance, then sampling is a fruitless exercise.
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.