Shinkansen fee

Hai there. I am planning to stay in japan for 13 days in dec.
I am going to nagano by shinkansen and to osaka by shinkansen from tokyo.
1. Is the shinkansen kagayaki and nozomi 9 include in the JR pass package?
2. I saw the price in the hyperdia that the shinkansen fare from tokyo to osaka is 8750 yen and there is additional seat fee of 5900 yen. Is that seat fee is compulsary to buy or we can just buy the 8750.

My route:
27 dec: jakarta tokyo by plain tokyo-osaka by train
28-29 dec : osaka
30-1 jan : kyoto
1-3 jan : tokyo
4 - 9 jan : nagano
9 jan: tokyo - jakarta

With my route is it worthed to buy the 14 days JR pass? I am just afraid that JR pass can not cover the whole trip while i am in japan.

Thanks.