I noticed that most buildings in Japan from all pre-modern periods were entirely build from wood. Even military installations.

Is there a historical reason for foregoing stone entirely? The castle walls themselves look to be very high quality stone work (suggesting availability of stone an the skill set to work it effectively) - so why not build the central keep and the wall towers from stone as well?

Wood seems to have a rather obvious disadvantage as a building material for military installations - wooden buildings burn easily. It is almost comical to read about various Japanese castles or temples, because inevitably there will be a point in history were the structure burned to the ground - sometimes for reasons easily avoidable, like Nijo Castle in Kyoto, which central keep burned to the ground because of a lightning strike.