JR Pass for 30 days, 5 places

Hello,

My wife and I will be in Japan starting for 30 days all in October, with Tokyo, then, Nagano, then Shizuoka (Mt. Fuji), Hamamatsu, then last stop Osaka.

My questions:

1. Will the JR Pass allow us to use the train to get us to those places?
2. Can we use the JR pass in the Tokyo Metro to get us to places around Tokyo? If not, what do we use for the within-Tokyo commute?
3. I understand that we have to buy the JR pass before we fly to Tokyo. Is this correct?
4. Is there a 30-day JR pass or we just buy a 21-day and a 7-day pass?

Thank you very much,

Rey