Shotokan is a style of compression and is described as "harder" Goju is described as hard and soft, Shito is more about bodily movement. Wado I'm not so sure of.
That would depend on how you split it up. You could divide them up as Okinawa, Japan and Korea based on their primary country. Or you could divide them up on the types in Okinawa, Shorin Ryu, Goju...
If you mean theater as in the building - they are proscenium, thrust, theater in the round, and created theaters.
If you mean styles of performance the most common answer is that there are two -...