How Many Days JR Pass Should I Buy?

Hi, my itinerary is as below:

26-31 Oct: Tokyo
31 Oct - 2 Nov: Fuji
2-6 Nov: Osaka
6-11 Nov: Kyoto
11-13 Nov: Oita
13-15 Nov: Nagasaki
15-16 Nov: Saga

Could you please advise how many days of JR Pass should I buy? As it seems like I only need it while travelling from Tokyo to Fuji, then Fuji to Osaka.
And also is the JR Pass shinkanshen include JR Pass Kyushu? OR is it two different JR Pass?