Clan Sawmill — what is it, how do I unlock it, who can build it, and how does it produce wood?

The Clan Sawmill is a clan automation station that produces wood for your clan automatically. You unlock it in the clan progression tree: the clan leader or an officer activates it there. It requires the previous progression level to be unlocked first and enough clan currency (which can be paid with coins), activation takes time and can be sped up for an extra cost. While running it consumes fuel and clan currency, and higher levels produce more wood in less time.