Answer from cs61c-cj (Peter Lau 16539384) for Question 2
1)  Any attempt to recreate artificial intelligence would require a finite state machine because the next step would depend on what was "learned" in the previous steps plus whatever is currently happening.  
2)  Gambling machines at casinos require finite state machines to calculate when to "give" the player a win (depending on when the last win was) and how much, depending on the initial bet.
3)  Complex encryption algorithms may also require a finite state machine.  An example would be the Enigma machine used by the Germans in World War 2 to encrypt messages.  Although it encoded letters one by one, the number of encoded letters changed the gears occassionally which influenced later encodings.