How to make elemental silicon?
Making elemental silicon is easy, but not for amateurs. Since it is cheap (~$2/kg) there is little reason to do this yourself.

Industrial processes do indeed mix silica with a source of carbon like coal. These react when very hot to give silicon. But the process usually uses an electric arc furnace and controlled conditions with carefully controlled use of gasses (including extra oxygen late in the process to enhance the amount of impurities that gather in the surface slag). It is unlikely that an amateur can easily reproduce this control.

You might get a result at lower temperatures using magnesium. But you will struggle to do this safely without some control of the atmosphere above the mix as magnesium will burn violently in air (or even in carbon dioxide). You might even need to use argon to blanket the mix as even nitrogen will react with magnesium.

So, basically, this is not something to contemplate as an amateur outside a well-equipped lab.