2 weeks in Japan

Hi,

I will be in Japan mid August. I plan on doing Tokyo (3 nights) > Kanazawa (2 night) > Stay in Kyoto (3 nights) and travel to Osaka & Nara > Kyoto hot spring (1 night) > Tokyo (4 nights)

I was wondering if the 7 day or 14 day JR Rail will be better? Will it also be useful in Tokyo too if I pick the 14 day one?

Can I access Shirakawa-go from the JR rail? Would it be possible to do a day trip there?

Since I have basically 7 days in Tokyo, if I decide to go to Nikko outside of the 7 day JR rail - how much would that be RT?

Thank you!