Is the Sun a big star or a small start compared to other stars in the galaxy?
Our Sun is an average sized star: there are smaller stars and larger stars, even up to 100 times larger. Many other solar systems have multiple suns, while ours just has one. Our Sun is 864,000 miles in diameter and 10,000 degrees Fahrenheit on the surface.
What's the biggest star in the known universe? The smallest?
Unfortunately the questions that you are asking do not have definitive answers. Because the vast majority of stars are very far away from Earth it is very difficult to precisely and accurately measure their properties. This is a very complex problem but I will try to put it in simple terms. Essentially, while we do know that larger stars emit more light than smaller stars our measurements only tell us the fraction of that light which reaches Earth - but this alone does not tell us how bright the star actually is because it will appear more or less bright in the sky depending on how far away away it is from Earth. Therefore, for an estimate of how bright a star is in absolute terms we also need to know how far away it is. And because this is difficult to measure we do not know for certain which star is the brightest. Nevertheless, the star Stephenson 2-18 with a radius that is approximately 2150 times larger than that of the Sun is currently our best guess regarding which of the known stars in the universe is the biggest.

As for the smallest star in the known universe, that question is even more difficult to answer. The first problem is that small stars are very dim which makes it much more difficult to detect them and to measure their properties. The second problem is that small stars are much more common than large stars so the number of possible candidates is immense and the likelihood of any of them being the correct answer is diminutively small. Even tiny uncertainties in our measurements make it impossible to answer this question with confidence so we unfortunately do not know the answer and most likely never will.