Use JR pass from Kyoto to Fuji, and best way to travel in Tokyo?

Hello,
I would love to get your advise on what pass to get:
This is our itinerary:
July 22 Tokyo Airport
4 night in Tokyo
July 26 travel from Tokyo to Takamara (with JR Pass??)
July 29 travel Takamara to Kyoto (with JR Pass??)
While in Kyoto day trip to Osaka and day trip to Nara
August 3rd travel from Kyoto to Mount Fuji area
August 5th travel from Mount Fuji area to Tokyo
August 12th Tokyo to airport

Is it possible to travel by train from Kyoto to Mount Fuji area? I cannot find it online?
Would you recommend to get a 14 day pass, because we stay longer in Tokyo during the last week?
And is there a separate pass to get from Tokyo airport to Tokyo city?
What is the best way to travel within Tokyo, is there a special pass as well?

Thank you so much for your advise :-)