I have a few questions regarding the production of pure, crystalline silicon:

As far as I know Silicon usually appears in nature in the form of sand or $\ce{SiO2}$ and then is split apart and brought into the form $ \ce{Si + 2CO} $ ; I am imagining now a hot glowing molten mass. However then I don't understand the following methods to separate the Si from the elements you don't want to have, like iron, carbon etc. How do you remove the impurities, why do those methods work?
For example you use a few other chemical reaction to bring Si into several other forms like $ \ce{HSiCl_3} $ and split them apart later on. I don't understand at the moment, how this helps to separate those materials as in: There is still this big mass with lots of different chemical connection you don't want to have.

I also lack an actual understanding of the Czochralski process to further purify your mass of silicon. I guess want has to accept that silicon likes to join pure crystalline silicon and adapt to its structure. However I don't see, why one is not using this method beforehand for example, if one already has raw silicon you get from splitting up $ \ce{SiO_2} $ if it works so greatly. And if it not does work so greatly, why don't you have other impurities ?